Taxonomy of BSPP fittings
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The facets identified for BSPP fittings are:

F-01

Geometry — straight, elbow (45°, 90°), tee (equal, reducing), cross, reducer (concentric, eccentric), cap, plug, union, nipple, hex bush, hose tail, etc. See Geometry Facet — Enumeration.

F-02

Gender — male, female, mixed (e.g., male × female elbow). Captures which end mates with what. See Facet — Gender.

F-03

Thread form — BSPP (the centre), BSPT, NPT (adjacent). The taxonomy does not enumerate every thread form globally; only those needed for confusion-avoidance. See Facet — Thread Form.

F-04

Nominal size — 1/8", 1/4", 3/8", 1/2", 3/4", 1", etc. Note the BSPP convention: nominal size refers to bore, not thread OD. See Facet — Nominal Size.

F-05

Sealing mechanism — bonded seal washer, O-ring, PTFE tape, anaerobic pipe sealant. The choice depends on thread form: BSPP (parallel) seals on a face or O-ring; BSPT and NPT (tapered) seal on the threads themselves. See Facet — Sealing Mechanism.

F-06

Material — brass (most common), stainless steel, plain steel, plastics (PP, PVC, nylon for low-pressure). See Facet — Material.

F-07

Pressure / temperature rating class — general purpose, high pressure, food grade, gas. Often expressed as a manufacturer's class or as a working-pressure number in bar. See Facet — Pressure and Temperature Rating.

F-08

Application context — plumbing (water), pneumatic (compressed air), hydraulic (oil, glycol), gas. Some facets (sealing mechanism, material, pressure rating) are constrained by application. See Facet — Application Context.

The promotion of one or two facets as primary navigation for end-user-facing selection guidance is a downstream design decision, recorded with rationale in ResearchJournal.org when it is taken.

The facets are nominally independent: any value combination is describable. In practice some combinations are excluded by physics or by trade convention:

• Plastic + high pressure is excluded by burst strength.
• BSPP + thread sealant only does not seal: BSPP requires a face seal (washer or O-ring), regardless of how much PTFE tape is added.
• Food-grade + plain steel is excluded by hygiene rules (food-grade requires stainless or food-grade brass).

These constraints are noted in the corresponding facet sections, not in a separate constraint table. The validation scenarios in Validation Scenarios exercise the confusion-avoidance constraints, which are the most instructive.

Standardised in ISO 228-1 and BS EN ISO 228. The thread is parallel (cylindrical), with a 55° symmetric Whitworth profile. Sealing is achieved by a face seal (bonded seal washer, O-ring) or by PTFE tape on combined sealing surfaces — not by the threads themselves.

Designation prefixes: G (e.g., G1/2 for 1/2-inch BSPP).

Standardised in ISO 7-1 and BS EN 10226-1. The thread is tapered (see The 1:16 taper, in plain numbers below for what that means), with a 55° Whitworth profile (same as BSPP). Sealing is achieved on the threads themselves with PTFE tape, pipe sealant, or anaerobic compound.

BSPT defines three designation prefixes, one male and two female. The pair to use depends on what is on the other side:

R

male, tapered. External thread tapered 1:16. The workhorse male BSPT thread. Example: R 1/2.

Rc

female, tapered. Internal thread tapered 1:16, mirroring the R male. This is the standard partner for R when both sides are dedicated tapered threads. The wedging action between the two tapers does most of the sealing work; the sealant fills the residual helical gap. Example: Rc 1/2.

Rp

female, parallel. Internal thread is cylindrical (not tapered), with the same 55° Whitworth profile and the same nominal size as the corresponding R male. Rp exists because cylindrical female threads are easier and cheaper to machine than tapered ones, especially in mass-produced bodies. The seal in an R × Rp joint relies more on thread sealant or PTFE tape filling the gap than on a wedging fit. Mechanically less robust under cycling than R × Rc, but very common in practice. Example: Rp 1/2.

So when shopping for "1/2-inch BSPT female", the user must distinguish Rc 1/2 from Rp 1/2: both are female, both are 1/2 inch, both are BSPT, but the internal thread is taper in one and parallel in the other.

Standardised in ANSI/ASME B1.20.1. The thread is tapered (1:16, same taper as BSPT), with a 60° symmetric profile. Sealing is on the threads with PTFE tape or pipe sealant.

Designation: NPT (e.g., 1/2 NPT).

Note on the side-by-side ambition for this section. The two figures above together do most of the visual comparison work the original I-01 ambition called for: the SVG above shows the modern Whitworth profile in technically-precise form; the Sellers plate shows the three historical thread forms in visual contrast even if not at modern measurement precision. A purely- modern side-by-side rendering of Whitworth 55° vs American 60° at the same scale remains a future illustration goal; see Catalogue.org and the BSPT taper geometry slot I-08.

Mismatching thread forms is the dominant cause of selection failure for non-specialists. The likely outcomes:

BSPP × BSPT

same thread profile (55° Whitworth), so they appear to engage. They will partially screw together, and may even tighten, but they will leak. The parallel and tapered profiles cannot achieve a thread-borne seal. Often discovered only after thermal cycling.

BSPP × NPT

different thread profile (55° vs 60°), so they engage badly: stripped threads, cross-threading, possible damage to one or both fittings. May force together under high torque, but the joint is not safe.

BSPT × NPT

similar tapered geometry but different profiles. Limited engagement, likely to leak; may seem to hold under low pressure.

Straight — two collinear ports. Carries the full gender facet (F-02): nipple (male × male), adapter (male × female), socket (female × female), reducing nipple, extender. The configuration space — gender × size × shape, plus dimensional specials — is shown in 4, with the internal through-bore in 5.

The straight facet carries a second configuration beside the nipple family: bsppfit_pipe(), a length of pipe of a given overall length with an independently gendered port at each end (see the Library Overview). Where the nipple is a short connector defined by its thread lengths, the Pipe is a long run of plain round stock defined by its length — the two are the short and long limits of the same two-port straight body. The Pipe has its own archetype gallery (variant gallery-archetypes, with a sectioned gallery-archetypes-cut companion) sweeping the four port-gender combinations against length and size. Topologically the nipple and the Pipe are the same object — a two-port tube — which is the starting observation of the Topological Foundations part below. The Pipe archetypes are shown in 6, sectioned in 7.

Elbow — two ports at an angle. Subtypes: 90°, 45°, male × male, female × female, male × female. Equal or reducing. The configuration space — gender × size × dimensional specials — is shown in 8, with the internal swept-bend bore in 9.

Tee (configuration of G-10 Manifold) — three ports, T-shaped. A configuration of G-10 Manifold, not a separate geometry class: the tee is the branch_count = 1 configuration of the unified branch-fitting class. Subtypes (equal tee, reducing tee) are recovered by setting size_run and size_branch independently on Manifold(). The trade name tee is preserved here as a configuration label; for the geometric description see G-10. Illustrated as the first cell of the Manifold archetype galleries: 22 (solid) and 23 (section).

Cross (configuration of G-10 Manifold) — four ports, +-shaped. A configuration of G-10 Manifold, not a separate geometry class: the cross is the branch_count = 1, branch_sides = "both" configuration of the unified branch-fitting class. The trade name cross is preserved here as a configuration label; for the geometric description see G-10. Illustrated as the second cell of the Manifold archetype galleries: 22 (solid) and 23 (section).

Reducer — changes nominal size. Concentric (same axis) or eccentric (offset; drains better in horizontal lines). The configuration space — gender × body shape × concentric/eccentric subtype — is shown in 10, with the internal conical size transition in 11.

Cap and plug — terminates a port. Cap goes over a male thread; plug goes into a female thread. This is the one geometry facet realised by two modules (bsppfit_cap(), bsppfit_plug()), a cap-and-plug pair. The cap's configuration space — size × head shape × head height — is shown in 12, with its internal female thread in 13; the plug's — size × head shape × thread length — in 14, with its solid male shaft in 15. The cutaways make the cap/plug duality concrete: the cap is hollow (female bore the male port enters), the plug is solid (male shaft entering a female port).

Union — detachable joint, three-piece (two halves plus collar nut), allows disassembly without rotating the whole pipe. The configuration space — pose (assembled vs exploded) × pipe-end gender × the single component pieces — is shown in 16, with the internal conical seat (the sealing geometry that is invisible from outside) in 17.

Hex bush (reducing bush) — short fitting that reduces from larger external thread to smaller internal thread. The configuration space — gender layout (M-large vs F-large) × size ratio × hex height — is shown in 18, with the through-bore and the diameter step at the gender transition in 19.

Hose tail (barb) — threaded fitting on one side, serrated barb on the other for hose attachment. The configuration space — barb profile × body shape × gender × barb count — is shown in 20, with the through-bore and the barb profile in section in 21.

Manifold — the unified branch-fitting class. A straight cylindrical run carrying one or more branch ports perpendicular to the run, plus a port at each end of the run. The trade categories tee, cross and manifold are all the same pipe-bodied geometry varying only in branch count and branch arrangement; they are recovered as configurations of this single class:

Tee

branch_count = 1, branch_sides = "one" — three ports (two run ends + one branch).

Cross

branch_count = 1, branch_sides = "both" — four ports (two run ends + two opposed branches).

Manifold

branch_count >= 2 — the multi-branch distribution forms.

In every configuration the run ends and the branches take per-port genders and sizes; the run may be open or capped at each end. History. Tee, Cross, and Manifold were originally three separate geometry classes; the continuum was found to be geometric rather than merely descriptive, and they were unified into this single class, with G-03 and G-04 retained only as configurations of G-10 and their model files marked deprecated. Non-orthogonal (Y-form) branches are supported via the branch_angle parameter (range 30..150 degrees, perpendicular at 90); all branches lean by the same angle (uniform tilt). The symmetric Y-fan form, where branches splay apart from a common stem, requires per- branch tilt and is a planned later enhancement. Distinction from a pneumatic distribution block — a solid rectangular bar with tapped ports — is deliberate: that is a different product family, not modelled here; G-10 covers the pipe-bodied form shown in supplier catalogues (HTC / PVC-Welt AV-810/820/830/850 and equivalents).

The configuration range — branch count and arrangement (recovering tee and cross), branch lean angle (Y- and X-forms), per-port gender, and capped/pointed run ends — is shown in 22, with the run bore and the branch-to-run junctions in 23. Because tee (G-03) and cross (G-04) are configurations of this class, these two galleries are where the Tee and Cross are illustrated: the first two cells of each figure are the tee (one branch) and the cross (one branch each side), so no separate G-03 or G-04 galleries exist.

Male (M)

external thread, smaller bore at the threaded end.

Female (F)

internal thread, larger bore at the threaded end.

Mixed

a fitting carries male on one port and female on another. Example: a male × female elbow.

The two-port shorthand "M × F" or "F × F" indicates the gender of each port. For three-port fittings (tees), all three ports are usually the same gender (typically female). Manufacturer catalogues sometimes use MF as a single token for "male × female".

Port order in shorthand is conventional but not standardised: for an elbow, "male × female" usually means the inlet is male and the outlet is female, but this should be confirmed visually before purchase.

• A single port cannot be both male and female.
• A male × male fitting (nipple) cannot self-mate; it requires two female-port mating fittings (sockets, valves, etc.).
• In confined spaces, gender choice may be forced by the orientation of adjacent fixed fittings (the user does not pick the gender; the existing assembly does).

• Buying two fittings of the same gender for a joint that needs opposing genders. Usually obvious on inspection; occasionally hidden when both fittings ship in covered packaging.
• Confusing Rp (BSPT female parallel) with Rc (BSPT female taper) at the same nominal designation. Both are "female" but seal differently.

• The size is given in inches even in metric countries; this is a historical fixture of the BSP family.
• Common sizes (smallest to largest): 1/8", 1/4", 3/8", 1/2", 3/4", 1", 1 1/4", 1 1/2", 2", 2 1/2", 3", 4". Domestic plumbing rarely exceeds 1".
• The actual thread OD for a given nominal size is larger than the nominal value. For example, G1/2 has a thread OD of approximately 20.96 mm; G1 has a thread OD of approximately 33.25 mm. ISO 228-1 specifies the exact dimensions.

• Two fittings of the same nominal size and same thread form mate by design. Mating two different nominal sizes is handled with a reducer (G-05) or a hex bush (G-08).
• A fitting marked "1/2" without thread-form context is ambiguous: it could be G1/2 (BSPP), R1/2 (BSPT), or 1/2 NPT. The thread-form designation is part of the size specification, not a separate dimension.

• Reading "1/2 inch BSP" off a tap and assuming the thread OD is 1/2 inch. The user then sources a fitting designed for G3/8 (whose thread OD is around 16.66 mm, closer to 1/2 inch). The fittings will not mate.
• Confusing nominal size with pipe schedule (wall thickness class). These are independent: a 1/2" pipe can be schedule 40 or schedule 80, with the same nominal size and outer diameter but different bore.

In France and parts of continental Europe, BSPP fittings are commonly designated by a pair of millimetre values rather than by the inch fraction — for example 15/21 for what ISO calls G1/2, or 20/27 for G3/4.

The two numbers are:

• the nominal bore in millimetres (the historical inside diameter of the iron pipe the fitting was sized for), followed by
• the nominal external thread diameter in millimetres, rounded to the nearest whole millimetre.

So 15/21 describes a fitting whose pipe bore is nominally 15 mm and whose male thread is nominally 21 mm in outer diameter. The exact thread OD per ISO 228-1 is 20.96 mm; the 21 in the European designation is that value rounded.

This makes the European notation more concrete than the inch-fraction form: both numbers are in real millimetres that the user can measure, while 1/2 alone refers to neither bore nor thread OD exactly. The two notations name the same thread; the choice between them is regional, not technical.

Equivalence between the two notations for the most common sizes:

Note: the rounded "second number" in the French form (12, 13, 17, 21, …) is thread OD rounded, not bore. Reading 15/21 as "15 inside, 21 outside (of the pipe)" is a common but incorrect mental model: the 21 is the male thread OD, not the pipe wall OD.

The dimension tables below give the standardised geometry of BSPP, BSPT, and NPT threads at the sizes commonly encountered in plumbing, pneumatic, and light-hydraulic service. Values are drawn from the relevant standards (ISO 228-1 for BSPP, ISO 7-1 for BSPT, ANSI/ASME B1.20.1 for NPT) and rounded to two decimals where the standard gives more precision.

What the columns mean.

Pitch

the axial distance between adjacent thread crests. Often quoted as threads per inch (TPI), the reciprocal of pitch in inches. Both forms are given.

Major OD

the diameter measured across the crests of the male thread. For BSPP this is constant along the length; for BSPT/NPT it is measured at the gauge plane (a defined position along the taper, near the start of the threaded section).

Minor diameter

the diameter measured across the thread roots of the male (equivalently, across the crests of the female). Useful for stress calculation and for visually distinguishing similar sizes.

Useful thread length

the typical effective thread engagement length for a hand-tight assembly, before any wrench-tightening allowance. Indicative; manufacturer catalogues vary.

Bonded seal washer (Dowty seal)

a flat washer with a metal outer ring and a rubber inner bonded to it. Compresses between the male fitting's flange and the female face. Used with BSPP and other parallel-thread fittings. Typical service limit: 200 bar, depending on rubber compound.

Figure 26: Cross-section of a bonded seal washer compressed under a hex-headed bolt. The outer hard annular ring (left callout) sets the compressed thickness and prevents the rubber from extruding under load; the inner soft annular ring (right callout) deforms to fill the surface asperities of both the bolt's underside and the tapped face, producing the seal. Diagram by Wikipedia user Brotherpete (created using Paint.net). Public domain, via Wikimedia Commons. See also Sources and Attributions.

O-ring

a circular elastomer ring seated in a groove on the male fitting's seat or under the head. Common in BSPP hydraulic fittings (e.g., banjo bolts). Typical service: varies by elastomer (NBR up to ~100 °C, FKM up to ~200 °C).

PTFE tape

thin polytetrafluoroethylene tape wrapped around male threads before assembly. Fills the helical gap and acts as both seal and lubricant. Used with BSPT, NPT, and combined sealing surfaces; not a substitute for a face seal on BSPP.

Anaerobic pipe sealant

liquid that polymerises in the absence of air and the presence of metal ions, filling thread gaps and locking the assembly. Used with BSPT and NPT, especially for gas service where PTFE tape is discouraged.

Cone seat (60° / 24°)

a metal-to-metal seal where the male fitting has a conical end that beds against a matching female cone. Common in hydraulic high-pressure connections; less common in plumbing.

Illustration: pending. The available candidate images conflate cone-seat sealing with adjacent-but-distinct mechanisms; a clearer cross-section is still being sought.

Gasket

a soft sacrificial part compressed between two mating faces to form the seal. The gasket deforms to fill the asperities of the two surfaces. Variants encountered in BSPP and adjacent fitting families:

Soft (fibre, elastomer, PTFE)

low-cost, used for cold water, room-temperature pneumatic, drainage. Not for steam or high-temperature service.

Composite (graphite, graphite-with-metal-mesh)

heat tolerant up to several hundred °C. Standard for steam, hot oil, exhaust.

Solid soft metal (copper, aluminium, soft steel)

single-use, crushed on first assembly. Used at very high pressure and at high temperature where neither elastomer nor composite suffices. Typically associated with flange or face-sealed fittings rather than threaded ones.

The flat-face crush case from earlier editions of this section is a soft-metal gasket; it is included here as one of the variants. A free-standing flat washer (such as a bonded seal) is also a kind of gasket but is listed separately above because the rubber-on-metal construction and the parallel-thread-only application are distinctive.

(1) Tape and anaerobic compounds do not seal a parallel thread, regardless of how much is applied. The taxonomy lists them with BSPP only when used as auxiliary thread lubricants, never as the primary seal.
(2) Face seals do not work on tapered threads: there is no flat face to seat against, and the tapered thread engagement already does the sealing.

• Wrapping PTFE tape on a BSPP fitting and expecting it to seal. The fitting tightens but seeps. The user rewraps, re-tightens, and damages the threads. The cure is a bonded seal washer or O-ring; the tape was the wrong mechanism, not the wrong amount.
• Using a bonded washer on a BSPT joint. The washer is compressed but the tapered geometry leaves gaps along the threads; the joint leaks.
• Reusing an O-ring after disassembly. Even an undamaged O-ring takes a compression set that may not re-seal at the same torque.

Brass

the dominant material for domestic and light industrial BSPP fittings. Easily machined, corrosion resistant in clean water service, available in dozens of manufactured forms. Standard alloys: CW617N (CZ132, dezincification-resistant: DZR brass) for potable water, CW614N (CZ121) for general use.

Nickel-plated brass

brass with a thin nickel coating for cosmetic finish and additional corrosion resistance. Otherwise behaves as brass.

Stainless steel

304 (general), 316 (marine, chemical service). Higher cost, higher pressure rating, broader chemical compatibility. Required for salt-water exposure and most food-grade applications.

Plain (carbon) steel

black or galvanised. Used for industrial steam, gas, and high-pressure water service. Susceptible to corrosion in wet service unless galvanised or coated.

Plastic (PP, PVC, CPVC, nylon)

low-pressure water, irrigation, drainage. PP is hot-water-capable; PVC is cold-water; CPVC is hot-water; nylon for compressed-air service at moderate pressure.

(*) Brass for natural gas service is acceptable in the UK and most of Europe but is forbidden by certain national regulations (e.g., some US jurisdictions). Always verify the local code.

Galvanic incompatibility

dissimilar metals in contact with an electrolyte form a galvanic cell; the more anodic metal corrodes preferentially. Brass against stainless in a salt-water environment will corrode the brass. Use a dielectric union to break the electrical path when mixing metals in wet service.

Dezincification

standard brass containing > 15% zinc can lose the zinc fraction in soft, low-pH water, leaving a porous copper structure that fails. DZR brass (CW617N or equivalent) is mandatory for potable water in many jurisdictions. Look for the marking DZR or CR on the fitting body.

Plastic creep

thermoplastics deform under sustained load. A plastic threaded fitting tightened to "metal feel" will continue to deform and may eventually crack. Tighten plastic to manufacturer-specified torque, not to feel.

The working pressure (also service pressure) is the maximum continuous pressure for which the fitting is rated. The burst pressure is significantly higher and is not a design target; the safety factor between working and burst is typically 4×.

Pressure ratings are temperature-dependent: a brass fitting rated for 16 bar at 30 °C may be rated for only 10 bar at 100 °C, because brass softens with temperature.

The terms low pressure, moderate pressure, and high pressure appear throughout this document. They are not universal definitions — they vary across industries, and a "high pressure" pneumatic line is well below a "low pressure" hydraulic line. The bands used in this taxonomy are the ones conventional in the plumbing / pneumatic / hydraulic literature for screwed-pipe fittings:

Where this taxonomy uses the bare word "high pressure" without further qualification, it means the 16-40 bar band. "Very high pressure" and "hydraulic pressure" are used for the higher band.

These ranges should be read as typical service envelopes, not as fitting capabilities. A particular brass elbow may be rated for 16 bar (the moderate band) but tested to a 64 bar burst; it still fails as a 25 bar fitting.

Domestic plumbing

6-10 bar at 65 °C. Adequate for mains water, central heating, hot water systems.

General industrial

16 bar at 100 °C. The "default" for most brass fittings sold in the EU.

High-pressure brass

25 bar at 120 °C, often DZR brass.

Hydraulic (steel/stainless)

100-400+ bar. Specified by hydraulic standard (ISO 8434, SAE J514) more than by fitting catalogue.

Gas service (yellow band)

pressure rating is set by the local gas code, not by the fitting alone. Fittings marked for gas often carry a yellow paint band on the hex.

• Pressure rating drops with temperature; verify the temperature-derated rating, not the headline number.
• Repeated thermal cycling can lower the effective rating beyond the static derating curve; gas and steam fittings should be inspected periodically.
• The weakest link in a joint sets its rating: a 25 bar brass elbow joined to a 10 bar plastic socket gives a 10 bar joint.

Plumbing (potable water)

domestic and light commercial water supply. Constraints: DZR brass or stainless required by most national codes; potable-water approval markings (WRAS, ACS, KTW, or the finer-grained DVGW W 534 for metallic fittings in Germany) typically required; pressure 6-10 bar at up to 90 °C.

Plumbing (drainage and waste)

gravity flow, low pressure. Constraints: chemical compatibility with household waste; usually plastic.

Heating (radiator and hydronic)

closed-loop hot water up to 100 °C. Brass and steel both common; air bleed and drain points use specific valve geometries (G-09 hose tail with cap is a common drain).

Pneumatic (compressed air)

clean dry air at 6-12 bar (the moderate band; see What "low", "moderate", and "high" pressure mean here). Constraints: low risk of corrosion (dry); plastic fittings are common; quick-release fittings often replace threaded joints downstream of the manifold (a multi-port distribution fitting).

Hydraulic (mineral oil, glycol)

very high pressure (100-400+ bar), narrow tolerance on cone-seat angles. Constraints: steel or stainless; ISO 8434 (DIN 2353) or SAE J514 fitting families dominate; cone-seat or O-ring face seal preferred over flat-washer.

Gas (natural gas, LPG)

typically tens of mbar to a few bar at the appliance (the low band). Constraints: national gas-code approval mandatory; brass with yellow band common in EU; some jurisdictions require steel; PTFE tape may be prohibited (anaerobic sealant required).

Thread form. Gas service strongly favours BSPT (R male into Rc female) because the tapered geometry seals on the threads themselves, with a thread-borne seal that is mechanically robust and resistant to vibration. BSPP with a soft-elastomer face seal is acceptable in some low-pressure appliance connections but is not the default for in-line gas fittings; many national codes restrict it. NPT serves the same role in markets where the American thread family dominates (notably the US).

Regional note — French metropolitan domestic practice. A trade-specialist report (heating engineer, France) describes the French domestic-plumbing convention as BSPP with a flat gasket for gas service, with filetage américain (NPT-style) not used for gas at all, only in limited non-gas situations. This diverges from the more general European preference for BSPT recorded above, and is consistent with the wider French preference for BSPP over BSPT in domestic plumbing (which the bilingual section also reflects: metropolitan French commercial vocabulary uses filetage gaz cylindrique as the everyday term). The divergence is national-code-driven (French regulations and installer training rather than thread-mechanics) and should be read as one regional practice among several, not as a contradiction of the European-default claim above.

Steam

high temperature (100-200+ °C), variable pressure. Constraints: steel or stainless; PTFE tape unsuitable (creeps under heat); composite or solid-metal gaskets and anaerobic sealants formulated for the operating temperature.

Thread form. Like gas service, steam favours BSPT (or NPT in American practice). The thread-borne seal tolerates the thermal cycling that would relax a face seal, and the absence of soft elastomers avoids the temperature-degradation problem entirely. BSPP with a metallic gasket is occasionally used at flange interfaces but is not standard for in-line steam fittings.

Food and beverage

clean-in-place (CIP) constraints, surface-finish requirements (Ra ≤ 0.8 µm typical for contact surfaces), often tri-clamp rather than threaded connections.

A fitting can be read two ways, and the document keeps both in view because they answer different questions and, revealingly, do not agree on everything. The fluid path (Framing I) looks at the negative space — the wetted surface bounding the bore. The solid body (Framing II) looks at the metal — the casting or bar stock with holes drilled in it. For a plain pipe these are nearly the same story; for a cap or a branched manifold they diverge sharply, and the divergence is itself one of the findings.

Before developing our own account, it is worth asking — as the project author rightly did — what others have already done with shapes of this kind. The exploration below was reached independently, but it turns out to sit at the confluence of two established bodies of work, neither of which appears to have been pointed at a BSPP fitting catalogue in quite this way. Knowing they exist both credits the prior art and tells us where the rigorous second pass should draw its tools.

Topology is the study of properties preserved under continuous deformation — stretching and bending, but never cutting or gluing. Two shapes are the same (homeomorphic) when one can be deformed into the other without tearing. The coffee-mug-and-doughnut cliché is exactly this: both have one handle, so a mug deforms into a torus.

The engineer's instinct already reaches for this when looking at the catalogue. An elbow "is just a bent pipe". A reducer "is just a pipe that gets narrower". A hose tail "is a pipe with one end dressed differently". These are deformation statements — claims that bending or tapering changes nothing essential. The question is: nothing essential to what? That is where we need an invariant.

Reading the catalogue (Taxonomy) through this single lens gives a strikingly simple table. The port count is the number of open mouths; deformation class groups the fittings that are plausibly inter-deformable without cutting.

Two things stand out immediately. First, the great majority of the catalogue — everything in G-01, G-02, G-05, G-08, G-09, and G-07 — has exactly two ports, and the "deformation note" for each is a genuine deformation: bend, taper, corrugate, none of which cuts or glues. Within the two-port class the hypothesis looks not merely plausible but obvious: these fittings really are deformations of one another, and of a plain pipe.

Second, the exceptions are exactly the two ways to leave that class: removing an end (the cap and plug, going to one port) and adding ends (the tee, cross, and manifolds, going to three or more). Both are changes of port count, and neither is a deformation. This is the first real finding, and it is already a tension for the "everything is a deformation of a pipe" hypothesis — which we now examine framing by framing.

Take the fitting to be its lumen — the connected open region a fluid fills. A plain pipe's fluid path is a circular cylinder: a tube, open at both ends. Topologically a tube is trivial — it is a deformation of a straight segment thickened slightly, or if we keep the open ends in view, a cylinder \(S^1 \times [0,1]\) whose two boundary circles are the ports.

Now take the fitting to be the material — the wall — with the bore as a tunnel bored through it. This is a different object with different invariants, and the hypothesis fares differently.

The agreement is the important part: under either accounting, the two-port fittings form a single deformation class containing the pipe, and both kinds of departure from it (sealing an end, adding a branch) are surgeries, not deformations. The hypothesis "every fitting is a deformation of a pipe" is therefore true on the two-port class and false off it, in both framings.

The divergences are instructive rather than contradictory. The fluid-path framing is blind to the wall (it cannot see the hex grip, and it cannot see that a union comes apart); the solid framing is blind to the lumen's role (it dignifies the pipe's own bore as a handle). For the question at hand — ancestry of the fittings as conduits — the fluid-path framing is arguably the more faithful, because a fitting's identity is its passage; but the solid framing is the one a printer and a stress analysis see. We are not yet forced to choose, and the parallel is cheap to maintain.

The loose pass above named the invariant — boundary-circle count — and conjectured a structure theorem (every fitting built from pipes, tees and caps). This pass makes that precise. It builds the cobordism category whose objects are the port mouths and whose morphisms are the fitting bodies, computes the invariants from the classification of surfaces, and — for the genus-zero family that is the entire BSPP catalogue — proves the structure theorem. The cobordism-category framing is standard (Atiyah 1988; Kock 2003 — see Bibliographic references (Topological Foundations)); what is original here is its instantiation on the BSPP fitting catalogue.

An object of the category is a compact one-dimensional manifold without boundary: a finite disjoint union of circles. We write \(\mathbf{n}\) for a chosen object with \(n\) circles, \(n \ge 0\), with \(\mathbf{0}\) the empty manifold. The circles are labelled (ordered), so that a morphism can record which port connects to which; unlabelled objects would lose the distinction between, say, a reducer's large and small ends.

Physically, one circle is one port mouth — the open rim a fluid crosses. An object is therefore a specification of how many open ends a fitting presents, and which is which. Nothing about diameter, thread, or gender lives at this level: those are decorations of a port treated in the decorations section below, not part of the topological object. The bare object is just "this many labelled circles".

A morphism \(\Sigma : \mathbf{m} \to \mathbf{n}\) is a compact oriented surface \(\Sigma\) whose oriented boundary is identified with \(\mathbf{m} \sqcup \mathbf{n}\) — the \(m\) circles designated incoming and the \(n\) circles outgoing. Such a surface is a cobordism from \(\mathbf{m}\) to \(\mathbf{n}\). Two morphisms are equal when there is an orientation-preserving homeomorphism between them fixing the boundary circles (a homeomorphism rel boundary). Equality of morphisms is exactly the loose pass's deformation: a bend or a taper is such a homeomorphism, so it does not change the morphism.

In the fluid-path framing \(\Sigma\) is the lumen wall, the surface swept by the passage, and its boundary circles are the port mouths. The incoming/outgoing split is a bookkeeping orientation, not a claim about flow direction: a fitting passes fluid either way, and reversing the arrow is the standard dual of a cobordism.

We now make precise why the table's surface column is well defined, and then prove the generation statement.

The topological object carries no diameter, thread, gender, taper, wrench grip, or barb. These are the substance of the manufacturing taxonomy, so it must be said precisely how they sit relative to the category, lest the rigorous pass seem to dissolve the very distinctions the library is built on.

Each is a decoration of a boundary circle or of the embedding, not a change of morphism:

• Gender (male thread / female socket) is a label on a boundary circle — a choice of how that mouth couples — with no effect on \((g, b)\). The four gender combinations of a two-port fitting are one morphism \(P_{0,2}\) with four different boundary labellings.
• Diameter and taper (reducer, hex bush) are the geometry of the homeomorphism, not the morphism: a reducer is the cylinder with a radius that varies along it, and "radius varying" is a homeomorphism, so the morphism is unchanged.
• Bend (elbow) is likewise a homeomorphism of the cylinder; the angle is geometry the topology forgets.
• Wrench grip (hex body) and barb (hose tail) are features of the solid wall, invisible to the fluid-path surface entirely.
• Detachability (union) is a decomposition of the assembled morphism into pieces; assembled, the union is \(P_{0,2}\) like any other two-port fitting.
• Branch position (where along a run a manifold's branches attach) is a decoration too, and less obvious than the others, so it is worth the argument. A manifold with its branches bunched at one point and the same manifold with the branches spread along the run are homeomorphic: the attachment points slide freely along the run without cutting or gluing, so the spreading is a continuous deformation and the morphism — the chain of pairs of pants \(P_{0,\,2+k}\) — is unchanged. Branch position is therefore geometry the topology forgets, exactly like a bend angle or a taper. This was confirmed in working code: carrying a per-port offset as optional decoration data let the bsppfit super-class emit a true multi-branch manifold — branches at different points along the run, bores all joined — with no change to its topological core, only the added decoration. The claim is thus not merely asserted but built.

So the topological category sees the skeleton of the catalogue — how many mouths, joined how — and the taxonomy's facets are the flesh: decorations of the mouths and geometry of the realising homeomorphism. The two descriptions are complementary, not rival. This is the exact sense in which the loose pass's "the topological grouping cuts across the geometric one" is true: the cut is the boundary between morphism (skeleton) and decoration (flesh).

The fluid-path framing gave a one-parameter family because a fitting's lumen is a surface and surfaces with boundary are classified by \((g, b)\). The solid-body framing — the fitting is the wall, a three-dimensional body with the bore as a tunnel — does not enjoy so small a classification.

A plain pipe's solid is a thick-walled tube: topologically a solid torus, genus one as a solid because the loop around the bore cannot be contracted within the material. A tee's solid is a thick-walled pair of pants; following its bores it carries more independent loops — higher genus as a solid. So in the solid framing the invariant is the genus of a handlebody, and the generators are handle attachments, the moves of three-dimensional handle theory. That theory exists and is standard, but it is heavier than the classification of surfaces, and it does not reduce the catalogue to one tidy integer parameter the way \(b\) does for surfaces: the relation between "number of ports" and "solid genus" is mediated by how the bores meet, which is more information than a single count.

This confirms the loose pass's provisional expectation, now with a reason: the rigorous treatment pays off for the fluid-path framing and is disproportionately costly for the solid-body framing. The conclusion is not that the solid framing is wrong — it is the right framing for wall thickness, printability and stress, none of which the fluid path can see — but that it is the wrong tool for the ancestry question. For ancestry, the fluid path's surface classification is what makes the question finite and answerable.

• The category is well defined and elementary. Objects are labelled circle-unions (port mouths); morphisms are oriented cobordisms (the fitting bodies) up to homeomorphism rel boundary (deformation); composition is gluing (screwing fittings together).
• Port count is a complete invariant, proved. Every fitting is genus zero, and a connected genus-zero surface is determined by its boundary-circle count \(b\). Hence the two-port fittings are provably mutually homeomorphic (one morphism, the identity tube), and crossing \(b\) is provably not a deformation.
• The structure theorem holds for the catalogue. Every fitting is a composition of the cylinder (pipe), the pair of pants (tee) and the disk (cap); a \(k\)-branch manifold is \(k\) pairs of pants. The G-10 tee/cross/manifold merge is a corollary.
• The decision is made: single ancestor. The cap and the tee are the same object \(P_{0,b}\) at \(b = 1\) and \(b = 3\), so the port-reducing and port-raising generators stand on one footing. The decorated super-class was then built (Models/bsppfit.scad), and the cap fell out of the same code path as the tee with no special pleading — the exit condition the loose pass set. The single-ancestor reading is thereby confirmed by working code: the catalogue is one family \(P_{0,b}\) decorated per port, and that family is the mono-file core the library is built on. The verdict is framing- relative (it rests on the fluid path) and adopted for cleanliness and fit, not compelled by the theorem — the right standard for a library.
• The framing asymmetry is now explained. The fluid path yields a one-parameter surface classification; the solid body needs three-dimensional handle theory and yields no single parameter. The fluid path is the framing for ancestry; the solid body is the framing for manufacturing.
• The decorations are placed. Gender, diameter, taper, bend, grip, barb and detachability are decorations of boundary circles or geometry of the realising homeomorphism — the flesh on the topological skeleton — so the rigorous pass refines the taxonomy rather than dissolving it.

The single-ancestor-versus-two-tier question was held open, with a crisp exit condition: build the decorated parametric super-class and see whether the cap slots into the same code path as the tee, with no special pleading. That build — Models/bsppfit.scad — is now done, and the exit condition is met. The decision is therefore no longer deferred. This section records it and its consequences.

The finding. A single bsppfit module, driven by a port list — each port a direction, gender, size, termination and optional offset — emits the whole catalogue from one code path: cap and plug (one port), pipe, nipple, elbow and reducer (two ports), tee (three), cross (four), and the one- and two-sided manifolds (a run with branches spread along it). The cap did slot in as cleanly as the tee: the two differ only in the port-list length and the termination flag, exactly as the structure theorem predicted for \(P_{0,1}\) versus \(P_{0,3}\). No fitting needed machinery another did not. Branch position, which a naive reading might have taken for structure, proved to be a decoration — a per-port offset — because a manifold with its branches bunched and one with them spread are homeomorphic; carrying the offset let the multi-branch manifold fall out of the same path with no change to the topological core.

The verdict. The evidence confirms the single-ancestor reading. The catalogue is one family — the genus-zero surfaces \(P_{0,b}\) — and each fitting is that family's general object at a fixed boundary-circle count \(b\), specialised by decorating its ports. The pipe is not the ancestor; it is the \(b = 2\) member, no more fundamental than the \(b = 1\) cap or the \(b = 3\) tee. The ancestor, if one insists on the word, is the parametric family \(P_{0,b}\) together with its gluing law: precisely a single parametric object, which is exactly what the bsppfit super-class is.

What this commits the library to. Single ancestor is now the architecture, not merely a stance. The mono-file bsppfit.scad becomes the core implementation, and the eleven dedicated trade models become thin sub-classes over it — each fixing a port list and adding its decoration — or are retired in its favour. This is the route to the long-held objective of reducing the model files toward a single core (ideal cardinality one). The sub-class layer is small and well understood: gender, size, angle and branch offset are decorations the super-class already carries as parameters, and only three fittings — the hex bush (a wrench-grip wall), the hose tail (a barb in place of a thread), and the union (a detachable three-piece assembly) — add a wall or assembly decoration the port list does not itself express.

What the decision honestly does not claim. The verdict is framing-relative: it rests on the fluid-path framing, whose genus-zero classification gives the clean one-parameter family. The solid-body framing, as The solid-body framing does not submit as cleanly records, offers no such tidy family, and an advocate of that framing would not feel the same pull. The single-ancestor reading is adopted because it is clean, matches the code, and is confirmed by a working build — not because it is forced by a theorem. That is the right standard for an engineering library: the factoring is sound and demonstrated, which is what the architecture needs.

The topology is not decoration on the library; it is the library's skeleton. The structure theorem says every fitting is a genus-zero surface fixed by its boundary-circle count and dressed with port decorations, and that is exactly the shape of the mono-file core: one bsppfit module, a port list selecting the boundary circles, and decoration parameters (gender, size, angle, offset) dressing them. What the topology calls a decoration the code carries as a parameter; what the topology calls the morphism the code carries as the port list. The dedicated trade models — Cap, Plug, Nipple, Pipe, Elbow, Reducer, Tee/Cross/Manifold, and the three decorated specials — are named configurations of that one object, retained as thin sub-classes (and as the reference oracle against which the mono-file is tested), not as independent geometry.

So the answer to "how many models are there, really?" is: one, with eleven names. The Taxonomy's engineering facets and this part's topological foundation meet here — the facets say how a fitting is described and selected; the topology says why one piece of code suffices to make them all.

The dimension along which BSPPFit goes beyond Wikipedia is not generic geometric vocabulary — Wikipedia's coverage of fitting types is broader than ours. The places BSPPFit goes deeper are:

• BSPP-specific designation (G, R, Rp, Rc) and the parallel-vs-tapered confusion analysis in F-03 and Mismatch consequences. Wikipedia covers BSP at general level in the dedicated British Standard Pipe article but does not integrate the designation explanation with the selection-decision context the way BSPPFit's F-03 section does.
• Per-size dimension tables. Wikipedia does not provide thread dimension tables; these would duplicate the ISO/BS paywalled standards. BSPPFit's per-size tables (BSPP, BSPT, NPT, plus the French DI×DE designations) are derived from open sources (Wikipédia FR Filetage gaz article, manufacturer catalogues, threadlib's CSV data) and provide the reader with concrete numbers that no Wikipedia article does.
• Selection scenarios. The validation scenarios SC-01..SC-09 in Validation Scenarios are selection problems ("you have a male hose-tail and a wall-mounted threaded port; how do you connect them?"). Wikipedia covers what each thing is but not which one to choose for situation X.
• Sealing-mechanism comparison in F-05 with pressure-rating bands and material constraints. The Bonded seal Wikipedia article covers the bonded washer in isolation; BSPPFit places it in the comparison context (vs O-ring, vs PTFE tape, vs anaerobic sealant, vs cone seat).
• French-trade vocabulary via the Bilingual Labels section. Wikipedia FR Filetage gaz covers French designation; BSPPFit's bilingual section integrates French with English at term-by-term granularity across all eight glossary sub-sections plus the French DI×DE sizing designations and DN code. No single Wikipedia article does this for BSPP.
• Parametric model library traceable to the taxonomy. Wikipedia is descriptive only; BSPPFit produces printable artefacts from the taxonomy's facet record. This is the largest single distinction and the largest remaining Phase 1 deliverable.

• Plastic fittings: ABS, PVC, CPVC, PEX. Phase 1 is BSPP-centred and brass-and-steel-centred; plastic fittings are Phase 2.
• Drainage and DWV (drain-waste-vent) fittings: P- trap geometry, sanitary tees, no-hub fittings. DWV fittings have BSPT-adjacent geometric vocabulary but a different sealing-mechanism universe (no pressure seal, just drainage); explicitly out of scope.
• Pigging-specific fittings: barred tee, lateral tee, full-port valves for pig passage. Pipeline-industry specialised; out of scope.
• Compression and flare fittings as primary subject matter: covered as adjacent classes for confusion- avoidance only. Wikipedia has dedicated articles (Compression fitting, Flare fitting) that go deeper.
• Slip couplings, rotary unions, dielectric unions: dielectric union is briefly mentioned in BSPPFit (F-06 Materials, glossary); slip and rotary are Wikipedia-only.

The Wikipedia article surfaces several useful items that should land in BSPPFit:

• 22.5° elbow in F-01 Geometry. Currently we list 90° and 45°; adding 22.5° is no cost and matches industry usage.
• Long-radius vs short-radius elbow as a length-of- curvature parameter (F-01 sub-axis). LR = 1.5×centreline-diameter, SR = 1×diameter. Affects pressure drop and pigging compatibility.
• Street elbow (one male, one female) as a gender-pair parameter. Could be a value of F-02 gender or a sub-type of F-01 elbow.
• Plumbing-vs-protractor angle clarification. The elbow's "45°" names the bend from straight, not the protractor angle of the joint. Worth a one- paragraph note in F-01 to prevent reader confusion.
• Wye as a separate F-01 entry distinct from Tee. Wye branches at 45° rather than 90°; semantically different from a 45° elbow plus a tee.
• Close nipple as a length-of-thread sub-variant of Nipple.

The facets F-01 through F-08 in Facet inventory were chosen empirically, as the project author and assistant worked through fittings and validation scenarios. They had not been checked against the discipline that the building- information classification standards enforce. The project author's rationale for doing the audit now, before the illustration pass: the domain has high combinatorics (the gender facet alone gives male x male, male x female, female x female for a two-port fitting), the model library so far covers only one combination per geometry class, and the taxonomy's facet structure should be shown sound before the modelling and illustration effort scales up. The audit is the step that gives confidence the facets are the right ones.

ISO 12006-2 (Building construction — Organization of information about construction works — Part 2: Framework for classification) is a meta-standard. It does not give classification codes; it specifies what classes of object a construction classification should have and how they relate. Its object classes include construction results, construction processes, construction resources (of which products are one), construction properties, and construction agents.

UniClass 2015 (published by NBS, United Kingdom) is a concrete classification implementing the ISO 12006-2 framework. It has eleven tables, each an independent and combinable facet of the construction domain: Complexes (Co), Entities (En), Activities (Ac), Spaces/Locations (SL), Elements/Functions (EF), Systems (Ss), Products (Pr), Tools and Equipment (TE), Roles (Ro), Materials (Ma), and Form of Information (FI). Each UniClass table uses a hierarchical four-pair numeric code (for example a product code of the form Pr_NN_NN_NN_NN).

The most important result of the audit is a level correction. UniClass's eleven tables are parallel facets of the whole construction domain. A BSPP fitting is a single kind of object within that domain: it is a Product. The whole of the BSPPFit taxonomy therefore sits inside one UniClass table — Products (Pr) — and more specifically inside the pipeline-and-fittings branch of that table.

The eight BSPPFit facets are consequently not parallel to UniClass's eleven tables. They are properties of a product, in the ISO 12006-2 sense of construction properties. The correct reading is:

• UniClass Products (Pr) table — the BSPPFit fittings are members of it.
• ISO 12006-2 construction properties — the BSPPFit facets F-01..F-08 are an enumeration of these for the specific product class "threaded pipe fitting".

This is not a defect in the taxonomy; it is a clarification of what the taxonomy is. BSPPFit is a deep, single- product-class taxonomy, not a breadth-first classification of the construction domain. The audit recommends stating this explicitly (done in this section) so that no future reader mistakes the F-01..F-08 facets for table-level peers of UniClass Co/En/Ac/…

Each BSPPFit facet is checked for orthogonality (can it be set independently of the others?) and mapped to the nearest ISO 12006-2 / UniClass concept.

The audit checked whether UniClass tables with no BSPPFit counterpart should become new facets.

• Activities (Ac) — install, maintain, test, replace. UniClass treats these as a table. BSPPFit scatters this content through F-08 and the validation scenarios. The audit recommends not adding an Activities facet: BSPPFit is a product taxonomy, and lifecycle activities are a separate dimension better left to the validation scenarios, which already exercise install-time and maintenance-time confusion.
• Tools and Equipment (TE) — spanners, torque wrenches, sealant applicators, thread gauges. The audit recommends not adding a Tools facet, for the same reason. Where a tool is taxonomically relevant (a thread gauge distinguishing BSPP from NPT) it is already mentioned in the relevant facet section.
• Connection type beyond threaded — compression, push-fit, solvent-weld, flanged. These are out of scope by the project's BSPP focus, deliberately. The audit recommends a single sentence recording that BSPPFit's F-01..F-08 describe threaded fittings and that the non-threaded connection families are a conscious exclusion, not an oversight.

UniClass and OmniClass use hierarchical numeric codes. The audit considered whether BSPPFit's flat F-01..F-08 facet numbers and G-01..G-09 geometry numbers should become hierarchical. Recommendation: not yet. The flat scheme is adequate at the current scale (eight facets, nine geometry classes). A hierarchical code earns its complexity when the enumerated space is large enough that a reader needs the code to navigate; BSPPFit is not there. The decision can be revisited if the variant space is fully enumerated.

The empirically-chosen facets F-01 through F-08 are sound. The audit produced no renumbering and no facet removal. Its results are clarifications, all recorded in this section and cross-referenced from the relevant facet sections:

1. BSPPFit is a deep single-product-class taxonomy; its facets are properties within UniClass Products (Pr), not table-level peers of UniClass's eleven tables.
2. F-02 Gender, F-03 Thread form, and F-04 Nominal size are per-port facets, indexed against a port schema that F-01 Geometry fixes. This names the combinatorial variant space precisely.
3. F-07 Pressure / temperature rating is a derived property, not a free facet.
4. F-08 Application context classifies typical use, not intrinsic form.
5. Activities and Tools are deliberately not adopted as facets; BSPPFit is a product taxonomy.
6. Non-threaded connection families are a conscious scope exclusion.
7. Hierarchical coding is not adopted at the current scale.

The single most useful result for the project's direction is the port schema concept (point 2): it converts the project author's qualitative concern about combinatorics into an explicit specification of the variant space, which the model library and the future illustration pass can both work against.

BSPP

British Standard Pipe Parallel. Parallel (cylindrical) thread, 55° Whitworth profile, designation prefix G. Sealed on the face, not the threads. Standardised in ISO 228-1.

BSPT

British Standard Pipe Taper. Tapered (1:16) thread, 55° Whitworth profile, designation prefixes R~/~Rp~/~Rc. Sealed on the threads. Standardised in ISO 7-1.

Designation prefix

the leading character(s) of a thread designation that identify its standard and form. G for BSPP; R~/~Rp~/~Rc for BSPT (male, female parallel, female taper); NPT for the American taper.

NPT

National Pipe Thread (American). Tapered (1:16) thread, 60° American profile. Sealed on the threads. Not interchangeable with BSPT despite similar taper.

Parallel thread

thread of constant diameter along its length. BSPP is parallel.

Pitch

the axial distance from one thread crest to the next. Often quoted as threads per inch (TPI) for inch threads.

R, Rc, Rp

BSPT designation prefixes. R is the male tapered thread; Rc is the female tapered thread (the standard partner for R); Rp is the female parallel thread (a cylindrical female of the same nominal size, used where a tapered female is impractical to machine).

Sellers profile

60° symmetric thread profile with truncated (flat) crests and roots. Proposed by William Sellers in 1864 as an improvement on Whitworth's 55° rounded profile, easier to machine. The basis of the United-States Standard thread family and, by descent, of NPT. Distinct from Whitworth profile in angle, crest geometry, and historical lineage.

Tapered thread

thread whose diameter changes along its length, allowing the threads to wedge together for sealing. BSPT and NPT are tapered.

Taper ratio

the rate at which a tapered thread's diameter decreases per unit length. BSPT and NPT both use 1:16 (i.e., the diameter decreases by 1 unit per 16 units of axial travel).

Whitworth profile

55° symmetric thread profile with rounded crests and roots. Used by BSPP and BSPT.

Adapter

a straight two-port fitting with one male end and one female end (M × F). In the straight family it is the mixed-gender counterpart of the nipple (M × M) and the socket (F × F); also sold as a "male × female connector". The same M × F gender configuration applies to other geometries (e.g. the M × F elbow, a "street elbow"); "adapter" names the straight instance specifically. Documented 0.56.0 (resolving the 0.8.5 open question on female and mixed-gender straight fittings).

Banjo bolt

a hollow bolt with a transverse passage, used with a banjo eye to make a swivelable hydraulic connection sealed by a bonded washer.

Bore

the inside diameter of a pipe or fitting passage — the cross-section through which fluid flows. Distinct from thread OD (the outside diameter of the thread on the fitting body) and from pipe OD (the outside diameter of the pipe wall).

Bushing (reducing bush)

a short fitting with a male thread on the outside and a smaller female thread on the inside. Used to step a port down by one or two nominal sizes in a single fitting.

Cap

a female closure that screws over a male thread to seal it. Distinct from a plug, which is the male counterpart that screws into a female port.

Figure 27: Cap, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 28: Cap, default variant, cutaway (BOSL2 BACK) showing the bore.

Coupling

a fitting that joins two pipes end-to-end. Generally female-female; the reducing coupling joins different sizes; the slip coupling omits the internal stop, used in repair work.

Cross

a four-port fitting with the three branch ports at 90° to the run. The plumbing equivalent of a tee with one extra outlet.

Figure 29: Cross, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 30: Cross, default variant, cutaway (BOSL2 BACK) showing the bore.

Elbow

a fitting that changes direction. Common angles: 90°, 45°, 22.5°. Long-radius (LR, centreline radius = 1.5×D) reduces pressure drop and entrained-solid deposition; short-radius (SR, = 1×D) fits in tight spaces and dominates pressurised systems. Both proportions are conventional standards (the multiplier is the pipe diameter D, not the thread diameter). Naming convention notes: "45° elbow" names the bend from straight, not the protractor angle of the joint — a clarification adopted via the Wikipedia coverage map.

Domain note (LR vs SR). The LR/SR distinction correlates with usage domain rather than being a free parameter:

• SR elbows are typical in pressurised systems and tight installations — threaded brass and steel BSPP / BSPT / NPT fittings in domestic plumbing, pneumatic, and light-hydraulic installations are predominantly SR.
• LR elbows are typical in low-pressure gravity-fed systems where low turbulence and minimum entrained-solid deposition matter — drain-waste-vent (DWV), sewage, central vacuum. LR elbows are commonly available in ABS, PVC, CPVC, and copper, not predominantly in BSPP-threaded brass.

Implication for BSPPFit scope. The LR/SR distinction is most-relevant outside the BSPP-centred scope. Within BSPP territory, SR is the default and LR is the special case; the classification is therefore recorded here as a property of an elbow rather than promoted to a separate facet axis. Whether LR/SR deserves its own facet remains open; deciding it in isolation would over-fit, and it is more likely to be resolved together with other length and curvature facets. Source for the materials and usage-domain pairing: Wikipedia Piping and plumbing fitting (informational, paraphrased).

Figure 31: Elbow, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 32: Elbow, default variant, cutaway (BOSL2 BACK) showing the bore.

Elbow, street

an elbow with one male port and one female port, allowing a male-female direction change in a single fitting. Equivalent to elbow with mixed gender applied; in BSPPFit's faceted model, a street elbow is F-01 = Elbow + F-02 = Mixed-gender, not a separate F-01 sub-type.

Fitting (generic)

any of the parts that join lengths of pipe or interface pipe to equipment: tees, elbows, couplings, unions, reducers, bushings, plugs, caps, hose tails, manifolds. The French equivalent raccord covers the same scope.

Hex bush

a bushing with a hexagonal external profile for spanner engagement.

Figure 33: Hex bush, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 34: Hex bush, default variant, cutaway (BOSL2 BACK) showing the bore.

Hose tail (barb)

a fitting with a threaded port on one side and a serrated barb on the other for hose attachment; usually retained by a worm-drive clamp.

Figure 35: Hose tail, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 36: Hose tail, default variant, cutaway (BOSL2 BACK) showing the bore.

Inlet

the port through which the working fluid enters a fitting. Tied to flow direction, not to a fixed end. Matters for direction-sensitive fittings (check valves, regulators) and for orienting asymmetric gendered fittings in an installation.

Manifold

a multi-port fitting consisting of a straight cylindrical pipe run (open or capped at each end) carrying one or more branch ports perpendicular or oblique to the run. In trade usage the term commonly names the multi-branch distribution form (a supply line feeding several consumers, or returns collected into one); in this project Manifold is also the name of the unified geometric class (G-10) of which the trade categories tee (one branch), cross (two opposed branches), and the multi-branch distribution manifold proper are all configurations — they share one parameterisable geometry and differ only in branch count and arrangement. Common downstream of a pneumatic compressor and upstream of individual tools. Distinct from a pneumatic distribution block (a solid rectangular bar with tapped ports), which is a different product family and not modelled here. Unified class adopted at 0.36.0; see the G-10 catalogue entry for the full history and parameter set.

Figure 37: Manifold, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 38: Manifold, default variant, cutaway (BOSL2 BACK) showing the bore.

Nipple

a short straight fitting with male threads on both ends (M × M). Used to extend a female-female chain. Length sub-variants exist (see close nipple). A "nipple" is male × male by definition; the mixed-gender straight fitting (M × F) is an adapter and the female-female straight fitting (F × F) is a socket — there is no fitting called a "female nipple", though the female-ended straight geometry exists under those other names. Resolved 0.56.0 from project-author trade observation (the F × F and M × F straight fittings are commercially available; they are named socket and adapter, not female nipple). The straight family thus spans the full gender facet.

Figure 39: Nipple, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 40: Nipple, default variant, cutaway (BOSL2 BACK) showing the bore.

Nipple, close

a nipple in which the threaded sections of the two ends meet without an unthreaded middle section — the threads of the two ends are continuous, with no separation. Used in tight-clearance installations where there is no room for the unthreaded middle band of a standard nipple. A close nipple is a length sub-variant of a nipple, not a separate fitting type; in BSPPFit's faceted model, a close nipple is F-01 = Nipple with a length parameter marked "close".

Outlet

the port through which the working fluid leaves a fitting. See Inlet.

Plug

a male closure that screws into a female port to seal it. Distinct from a cap, which is the female counterpart that screws over a male thread.

Figure 41: Plug, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 42: Plug, default variant, cutaway (BOSL2 BACK) showing the bore.

Port

the threaded opening of a fitting, valve, or appliance. A fitting has at least two ports; tees, crosses and manifolds have more.

Reducer

a fitting that changes nominal size between two ports. Concentric keeps the centreline straight; eccentric offsets one port to keep one bore wall continuous (drains better in horizontal lines).

Figure 43: Reducer, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 44: Reducer, default variant, cutaway (BOSL2 BACK) showing the bore.

Socket

a short straight fitting with female threads on both ends. Used to join two male-ended fittings.

Tee

a three-port fitting with the branch at 90° from the run. Equal tee has all three ports the same size; reducing tee has the branch stepped down. Distinct from a wye (45° branch).

Figure 45: Tee, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 46: Tee, default variant, cutaway (BOSL2 BACK) showing the bore.

Union

a three-piece detachable joint allowing the joint to be undone without rotating the connected pipework. The three pieces are two halves with mating seat surfaces plus a collar nut that draws them together.

Figure 47: Union, default variant (single fitting; viewpoint lat 35°, lon 270°). Solid form.

Figure 48: Union, default variant, cutaway (BOSL2 BACK) showing the bore.

Wye

a three-port fitting with the branch at 45° from the run, common in drainage applications. Distinct from a tee (90° branch). Surfaced as a borrow-candidate from the Wikipedia coverage map; see Coverage map vs Wikipedia.

Female

internal (inside) thread.

Male

external (outside) thread.

Mixed gender (M × F)

a fitting with one male and one female port.

Anaerobic pipe sealant

liquid sealant that polymerises in the absence of air and the presence of metal, locking and sealing threaded joints. Sometimes called by trade names (Loctite 577 and similar).

Bonded seal washer (Dowty seal)

a washer with a rubber inner bonded to a metal outer ring, used to seal a parallel-thread fitting against a flat face.

Compression set

the loss of resilience an elastomer suffers after sustained compression; an O-ring with high compression set may not re-seal after disassembly and reassembly.

Cone seat

a metal-to-metal seal where a conical male end beds against a matching female cone. Common at 60° in hydraulics.

Gasket

a soft sacrificial part compressed between two mating faces to form a seal. May be soft (fibre, elastomer, PTFE) for low-temperature service, composite (graphite, graphite-with-metal-mesh) for steam and hot service, or soft metal (copper, aluminium) for very high pressure or temperature.

O-ring

a circular elastomer ring seated in a groove, compressed to form a seal.

PTFE tape (plumber's tape, Teflon tape)

thin polytetrafluoroethylene tape wrapped around male threads before assembly. Acts as a thread filler and lubricant on tapered threads.

CW614N / CW617N

standard EN designations for the two most common BSPP brass alloys. CW614N is general-purpose; CW617N is DZR.

Dezincification

corrosion process by which zinc is selectively leached from standard brass, leaving a porous copper structure; aggravated by soft, low-pH water.

Dielectric union

a union with an insulating insert that breaks the electrical path between dissimilar metals to prevent galvanic corrosion.

DZR brass

dezincification-resistant brass (CW617N or equivalent); marked DZR or CR on the fitting body. Required for potable water in many jurisdictions.

Galvanic corrosion

accelerated corrosion of one metal when in electrical contact with a more noble metal in the presence of an electrolyte.

Galvanised steel

carbon steel with a zinc coating for corrosion protection. Used for general plumbing and gas in many markets.

Burst pressure

the pressure at which a fitting will fail. Typically 4× the working pressure; not a design target.

High pressure

in this taxonomy, the 16-40 bar band (heavy pneumatic, light hydraulic, high-pressure water). Very high pressure is the 40-400+ bar band of industrial hydraulics. See What "low", "moderate", and "high" pressure mean here.

Low pressure

in this taxonomy, the 1-6 bar band (domestic plumbing, irrigation, central heating). The sub-band below 1 bar is very low (gravity drainage).

Moderate pressure

in this taxonomy, the 6-16 bar band (light pneumatic, mains plumbing, general industrial water).

Pipe class

collective term for the combination of pressure rating, schedule, and material that defines a pipe's service envelope.

PN16, PN25, PN40

nominal-pressure markings: 16 bar, 25 bar, 40 bar respectively. The PN system is European; the American equivalent is class (e.g., Class 150, Class 300).

Pressure derating

the reduction in working pressure as temperature rises. Brass and plastic derate sharply; steel and stainless less so.

Schedule (Sch)

a pipe wall-thickness class. Schedule 40 is the most common in domestic plumbing; higher numbers indicate thicker walls. Independent from nominal size.

Working pressure

the maximum continuous pressure for which a fitting is rated. Synonym: service pressure.

3.1

EN 10204 3.1 material certificate; documents the specific material composition and test results for a batch of fittings.

ACS

Attestation de Conformité Sanitaire (France). French potable-water approval.

DVGW W 534

German potable-water approval specifically for metallic and combination drinking-water fittings (DVGW = Deutscher Verein des Gas- und Wasserfaches, the German technical-scientific association for gas and water). Where KTW is the broader plastics- in-contact-with-drinking-water umbrella, this approval is finer-grained: it applies to threaded brass fittings, valves, and similar metallic items intended for installation in domestic drinking-water systems. Encountered on French supplier catalogues that distribute German-made fittings.

KTW

Kunststoffe-Trinkwasser (Germany). German potable-water approval.

WRAS

Water Regulations Advisory Scheme (UK). Marks a fitting as approved for potable water in the UK.

Compression fitting

a non-threaded fitting that seals on a metal ferrule compressed against the pipe by a nut. Common in copper pipework. Out of scope for Phase 1; in scope for Phase 2.

Hydraulic

relating to liquid (oil, water-glycol) under high pressure; typically 100-400+ bar service.

Pneumatic

relating to compressed air or other gas transmission; typically 6-12 bar service.

Quick-release fitting

a non-threaded fitting that mates by push or twist. Common in pneumatics; out of scope for Phase 1 (threaded fittings).

Tri-clamp (sanitary clamp)

a non-threaded connection used in food and pharma; a gasket between two polished ferrules clamped together. Not part of the present BSPP taxonomy but listed here because users coming from food/pharma contexts often confuse it with threaded BSPP.

Region-specific names are noted in parentheses. Where two names exist for the same thing the entry lists both, with a cross-reference.

Faucet

North-American synonym for tap (water outlet) in the kitchen-and-bathroom sense. See Tap.

Hose clamp

Commonwealth synonym for worm-drive clamp. North-American hose clamp is the same thing. See Worm-drive clamp.

Hose clip

British colloquial synonym for worm-drive clamp, especially in the smaller sizes. See Worm-drive clamp.

Jubilee clip

British trade-name-as-argot for a worm-drive clamp. Jubilee Clip is a registered trademark (L. Robinson & Co.) but the term is used generically across UK plumbing and automotive trades. See Worm-drive clamp.

Plumber's argot — "leak"

in plumbing trade speech a joint seeps if it lets through a small steady wet trace, weeps if the loss is barely visible, and leaks if there is observable flow. The taxonomy uses "seeps" and "leaks" in the same way.

Shutoff tap

a tap used to interrupt flow in a pipework run, typically a quarter-turn ball or gate valve. North-American synonym: shutoff valve. The "tap" sense here is the British/general-English valve-as-tap, not the kitchen faucet sense. See Tap.

Shutoff valve

North-American synonym for shutoff tap. See Shutoff tap.

Spigot

outdoor-water-outlet synonym used in North America ("garden spigot"). In British English spigot can also denote a plain unthreaded male end of a pipe intended to be inserted into a socket; context disambiguates.

Stopcock

British plumbing term for a shutoff tap installed on the supply side of a building or major branch. North-American synonym: main shutoff valve. See Shutoff tap.

Tap

in this document, generic for a manually operated valve fitted into a pipework run — a faucet in North-American English, or a shutoff valve when its role is to interrupt flow rather than dispense it. The British and general-English tap covers both senses; where the distinction matters the document uses shutoff tap explicitly.

Worm-drive clamp

a band-and-screw clamp used to secure a flexible hose onto a barbed fitting (G-09 hose tail). The slotted band is tightened by a captive screw whose helical lip engages the slots in the band. Sizes are quoted as a clamping-diameter range (e.g., 12-22 mm). Regional synonyms: Jubilee clip (UK), hose clamp (Commonwealth and North America), hose clip (UK colloquial).

Figure 49: Three hose-clamping mechanisms photographed side by side. Top right: a worm-drive clamp (the slotted band with captive screw whose helical lip engages the band's slots). Left: a wing-nut style clamp shown installed on a hose tail with hose attached. Bottom right: a small two-bolt clamp closing on a copper-coloured hose end. The worm-drive form (top right) is the most common in plumbing and automotive use; the smaller forms appear in petrochemical and pneumatic service. Photograph by Peter Felecan, project author. See also Sources and Attributions.

In metropolitan-French plumbing trade, BSPP sizes are conventionally written as the pair diamètre intérieur × diamètre extérieur du filetage in millimetres (e.g. 15 × 21), rather than by the BSPP G-designator (e.g. G1/2) or the European DN designator (e.g. DN 15). The DI×DE form is a presentation convention, not a separate thread standard: a fitting marked 15 × 21 is the same physical fitting as one marked G1/2 or DN 15; only the labelling differs.

No "15/21 family". The phrase "the French 15/21 family" is not established trade vocabulary — French commercial sources use "norme", "dimension", "format", "désignation métrique", or simply "15/21", not "famille". Use "DI×DE designation" or "DN designation" depending on which is meant.

Three coexisting designation systems. The same physical half-inch BSPP thread carries three different labels in different European contexts:

• BSPP G-designator, e.g. G1/2. The standard ISO 228 mark; appears engraved on machined fittings across Europe.
• European DN designator, e.g. DN 15. The diamètre nominal system of ISO 6708, used as a code across European catalogues. Not a physical measurement — ISO 6708 says explicitly that the number "is used for reference purposes" and only approximates a diameter.
• French DI×DE designation, e.g. 15 × 21 or 15/21. Dual-mm notation: 15 mm approximate inside diameter of the pipe + 21 mm approximate thread outer diameter. Vivid in French domestic-plumbing packaging; less common in German or northern-European catalogues.

Cross-reference between the three is exact for any given fitting; the table below records the standard correspondences.

Why not "Imperial". Labelling the second column Imperial would be historically defensible (the G-designator's number is the legacy half-inch nominal-bore from before thread-standard separation) but misleading: G1/2 is the BSPP designator under the modern ISO 228 metric standard, and reading "1/2" as "half an inch" is exactly the confusion the F-04 Nominal Size section warns against. The column header is therefore BSPP designator, not Imperial.

Is this only French? The DI×DE form is metropolitan-French specifically. The DN form is general European (ISO 6708; widely used in Germany, Italy, Netherlands, etc.). The G-designator is universal across the BSPP world. German practice illustrates the contrast: a German fitting catalogue typically lists a ½-inch BSPP thread as G 1/2 Zoll, DN 15, 1/2" AG (where AG = Außengewinde, "external thread"); the /15 × 21/ form is rare in German commercial use. French commercial use, by contrast, frequently shows only the DI×DE form on packaging — which is the identification problem this section addresses.

Note: the DN number approximates the inside diameter in millimetres (DN 15 ≈ 15 mm bore); the French-DI×DE-first-number is the same approximation under a different label. Neither is a precise physical measurement: actual bore depends on pipe wall thickness, which depends on pipe class. The second number in the French form (the 21 in 15 × 21) is the rounded thread outer diameter, not the pipe outer wall diameter — a common confusion. See F-04 §Bore and thread-OD notation for the full discussion of 15/21 as bore and thread OD, and Facet — Nominal Size for why the nominal label and the physical measurement diverge.

The metropolitan-French identification workflow remains: read the DI×DE designation off the fitting → cross- reference this table → find the BSPP G-designator → look up the per-size dimension table in F-04. German catalogues typically print all three labels on the same fitting, so the cross-reference is implicit.

• Pipe materials beyond brass and steel. The PVC, PEX, polyethylene, and copper sweat-fitting vocabularies are within plumbing's broader French terminology but out of scope for BSPP-centred BSPPFit.
• Hydraulic / pneumatic specialised vocabulary beyond what intersects with BSPP fittings.
• Sanitary fittings (DIN 11581 etc.) which have their own French vocabulary.
• Items flagged [à vérifier] above remain pending project-author verification against the workbench; corrections welcome as journal entries.

The Topological Foundations part draws on standard sources in topology; they are listed here, with the inline markers in that part pointing to this section, per the project convention of inline attribution plus a collected list. The cobordism and Frobenius-algebra framing is standard; what is original is its instantiation on the BSPP fitting catalogue.

• Michael F. Atiyah, Topological quantum field theories, Publications Mathématiques de l'IHÉS 68 (1988), 175–186. The TQFT axioms casting a field theory as a functor from a cobordism category — the source of the "objects are manifolds, morphisms are cobordisms" reading of fittings.
• Joachim Kock, Frobenius Algebras and 2-D Topological Quantum Field Theories, London Mathematical Society Student Texts 59, Cambridge University Press, 2003. The textbook treatment of the two-dimensional cobordism category, the pair of pants as generator, and the equivalence of 2D TQFTs with commutative Frobenius algebras.
• Lowell Abrams, Two-dimensional topological quantum field theories and Frobenius algebras, Journal of Knot Theory and its Ramifications 5 (1996), 569–587. The presentation of the two-dimensional cobordism category by generators and relations.

• Jean Gallier and Dianna Xu, A Guide to the Classification Theorem for Compact Surfaces, Geometry and Computing 9, Springer-Verlag,

  1. The classification of compact surfaces (with and without

  boundary) by genus and boundary-circle count.

• William S. Massey, A Basic Course in Algebraic Topology, Graduate Texts in Mathematics 127, Springer-Verlag, 1991. Standard reference for the classification of surfaces and the genus invariant.
• For the engineering reading — pipe networks as graphs whose nodes carry a valence (a plain pipe degree two, a branch degree three or more) — the framing is common to the hydraulic-network and CAD feature-recognition literature rather than owed to one canonical work, but two significant sources ground it:
  • On the hydraulic side, Hardy Cross, Analysis of Flow in Networks of Conduits or Conductors, University of Illinois Engineering Experiment Station, Bulletin 286 (1936), is the foundational treatment of a pipe network as a graph with conservation of flow at each junction node — the first practical engineering method for looped pipe networks.
  • On the solid-modelling side, Kevin Weiler, Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments, IEEE Computer Graphics and Applications 5 (1985), no. 1, 21–40, represents a solid as a face-adjacency graph — the discrete structure behind the solid-body framing's "graph of faces and adjacencies".