Geodesic timber dome

A timber-strut geodesic dome you can build: pick how finely the sphere is divided and how much of it stands, give a radius or the floor area you need, and read off how many struts of each length to saw, how many metres of timber that is, and how many hubs of each kind to make. The struts stand on edge, each end sawn with a mitre and a kerf that takes a laser-cut steel fin, two bolts through it; the fins weld to a short steel tube between two laser-cut cap plates. The plates go to the laser as one sheet.

What it shows

• A table drives the structure. table.set holds the published chord factors, strut counts, hub counts and face counts for each dome (dome_types), and variable.publish with choicesFrom offers them in the form. The strut lengths are the published factor times the radius; the factors are read from the table, not calculated.
• Everything recomputed from the geometry. The hub positions are built by formula: icosahedron corners from its closed-form coordinates, class I subdivision by whole-number weights, each point pushed out to the sphere. An assertion per strut type and frequency compares the distance between two such hub points with the published chord factor in the table (to the table's five decimals).
• Symmetry keeps it small. feature.mirror and a 5-fold feature.pattern build a sector from its fundamental domain: 4, 9 or 20 struts stand for the 25 to 165 of the dome. Each strut is one feature.transform of a master strut, its rotation worked out in formulas from the two hub points; the transforms copy one strut, one set of fins and bolts and one hub. No booleans join the struts, so 3V stays light.
• Formulas for ranges. The radius range follows from the dome type and the strut (radius_min_formula, radius_max_formula): the shortest strut must hold both fins and their bolts and not be stubby, the longest must come out of 4.8 m stock and keep its weak-axis slenderness within 180. The floor-area range follows the same limits, and the plate thickness is capped by the cheek the strut keeps beside the kerf.
• Structure from the form. The dome type changes the number of struts, hubs, strut types and the whole shape.
• Masters stay out of sight. The master strut, fin, bolt and hub at the origin are hidden with feature.visible; they are what the transforms copy and what the cut sheet draws.
• A cut sheet and templates. set.define gives Hub plates to laser cut (one fin per strut type, one cap plate, one anchor plate) and Strut templates (each strut's wide face with its four bolt holes, between the short points of the mitres; the mitre and the kerf are outputs). A static model could not give this schedule.

The real thing

Chord factors and counts. Published chord factors, each verified at the row's strut count:

Strut length = radius × chord factor, the two hub centres apart. Domerama's chart gives the 3V factors for the 3/8; the 5/8 dome uses the same three lengths in the counts Desert Domes lists.

The base of a 3V dome is not quite flat. The 3V icosahedral subdivision (method 1, three chord factors) has no ring of hubs at one height: the base hubs of the 3/8 sit at two levels, 1.6 % of the radius apart, and so do those of the 5/8. Flat-base variants exist (Kruschke's, with four lengths) but they are other domes with other chord factors. This Jig keeps the published three-length dome and says what it costs: 5 of the 15 base hubs of the 3/8 and 10 of the 15 of the 5/8 stand on the higher level, by the output height difference between the two levels (56 mm at the default radius, more than a shim on a big dome). So every base hub stands on a seat: an anchor plate bolted to the ring and a 40 mm post welded under the tube, the posts of the higher hubs taller by that difference (the outputs give both lengths). The 1V and 2V domes have flat bases.

The strut. The sections on the form are the common CLS (38 x 89, 38 x 140 mm) and sawn structural sizes: check your supplier. Sawn timber on edge (depth along the sphere's radius), arrises eased, each end cut with two mitres in plan at half the tightest strut angle at any hub of that dome (between 54.6° and 60° between struts, so about 27° to 30° each side, the output Mitre), and below mid-depth the end is cut back parallel to the hub axis so that it clears the tube. A full-depth saw kerf 2 mm wider than the fin plate takes the fin, as long as the output Saw kerf: length. The saw length is the strut's length over the long points of its mitres, the length to cut the timber to before mitring (the output saw length); the kerf then takes the very point away, so a finished strut measures a kerf-width divided by tan(mitre) less, and that is what the model is measured against. The short points on the wide faces are the other output (and the template). Density is C24 spruce at 420 kg/m³ (mean density of EN 338, as listed in Taylor Maxwell's strength data).

The connection. A laser-cut steel fin in the plane of the strut and the sphere's centre goes into the kerf and takes two bolts through strut and fin in double shear. The bolt is M12 in timber at least 45 mm thick and 140 mm deep and M10 otherwise; each cheek keeps at least 1.5 bolt diameters of timber beside the kerf, which caps the plate thickness (a proportion rule of this Jig, not a clause of a standard). Spacing and distances follow EN 1995-1-1:2004+A1:2008 table 8.4 for bolts (read in the standard, and as summarised by Roy Mech), for load along the grain: along the grain between bolts a₁ = (4 + |cos α|) d = 5 d, loaded end a₃,t = max(7 d; 80 mm), unloaded edge a₄,c = 3 d. The end distance is measured to the short corner of the mitred cheek, not to the tip. Clause 10.4.3 gives the holes (at most d + 1 mm in timber, at most d + max(2 mm; 0.1 d) in steel) and the washers (at least 3 d across and 0.3 d thick; here M10: 30 mm × 3 mm, M12: 37 mm × 4 mm). The bolt is modelled as one solid, a washer as wide as the block with the hexagon head (ISO 4017 k: 6.4, 7.5 mm) at one end and the nut (ISO 4032 m: 8.4, 10.8 mm, as listed by Würth and Kramp) at the other. The output gives the length to order: strut, two washers, nut and two thread pitches, rounded up to 10 mm.

The hub. Round steel tube (CHS 60.3 × 4 mm for 38 mm struts, 76.1 × 4 mm for thicker ones; both are cold-formed EN 10219 sections, see Eurocode Applied for their properties) as long as the fin is deep plus 60 mm, along the sphere's radius, with a 10 mm flanged laser-cut cap plate on each end. The fins stop 2 mm from the tube (the weld gap) and the strut ends stop 20 mm further, so that the fin can be welded all round; between the two closest fins at a tube at least 15 mm stays open for the torch (measured). All steel is hot-dip galvanised. The fin plates are one shape per strut type; the caps are plain discs without fin slots, so the fins are set out on the tube by angle. The angles depend only on the dome type, not on its size. Read each row clockwise, seen from outside the dome with the cap towards you; a base hub starts at the first fin after its open side, which faces the ground. "A 55.7 B" means fin A, then 55.7° clockwise to fin B. Most rows read the same either way round. Three base rows do not: their hubs come in two hands, which are mirror images and are not interchangeable, so weld five of each.

Round the base ring the two hands alternate. On the 2V every second hub is hand 1. On both 3V domes, walking counter-clockwise seen from above from an all-C base hub, the next hub is hand 2, the one after it hand 1, then the next all-C hub.

This table was computed outside the document (a script run once on the same subdivision, not in this repository) and copied here; nothing in the Jig produces or checks it row by row. AGENTS.md §3 wants what a Jig decides to live in the document, and 3DCraft has no way to show a per-hub table in the form. The form computes and shows only the smallest and largest fin angle of the dome you set. Tack the fins with a protractor or a printed disc, and check them by dry-assembling a ring of struts before the final welds.

Making it. Saw the struts to the saw length in the form and cut both mitres so that their long point is at the end (the arris eased, the lower half of the end cut back at the axial angle); band-saw the kerf at both ends to the kerf length; drill the holes from the template, measured from the short point. Laser cut the fins and caps and tack them onto the tube with the fins in their planes; weld; galvanise. Bolt the struts to the hubs on the ground ring by ring from the top down (or bottom up with a centre pole). Weld a seat post under each base hub, bolt its anchor plate (4 × M12) to the ring; on a 3V dome the taller posts go under the hubs of the higher level. Skin, roof and glazing are not part of this Jig.

Scale figure. The silhouette beside the dome is 1.75 m tall and is not built.

Budget at 3V. Nothing is switched off with frequency: every strut, fin, bolt and hub is drawn at 1V, 2V and 3V. It holds because the struts are not joined into one body: each is a transform, a 5-fold pattern and a mirror of that pattern (no booleans).

Parameters

Outputs: for A, B and C the count, the saw length (long point to long point of the mitres) and the short-point length; struts, total; timber to buy in metres at saw length; the mitre angle, the kerf length and width; hubs total and the 4-, 5- and 6-way counts; the tube's outside diameter, wall and length; the smallest and largest fin angle; fin, cap and anchor plates to cut; bolts, their diameter and the length to order; radius; height above the ground; floor diameter and area; the level difference of the base and how many hubs stand on the higher level; the seat post's diameter and its two lengths; the mass of the struts and of the steel (hubs, fins, bolts and seats).

Checks

The assertions: Euler's formula for an open dome (hubs − struts + faces = 1); the strut count and hub count of the table found again in the model (bolt holes in the timber, hub tube walls); the volume of all the placed timber equal to the schedule times the master struts; each strut type's chord factor from the hub geometry against the table; hub types adding up (4 n₄ + 5 n₅ + 6 n₆ = 2 × struts); for every strut of the fundamental domain the distance from its orbit to the hub body at one of its ends (every hub class is covered), at most the closed-form gap of that end plus 0.5 mm and at least 0.35 of it (the kernel cannot prove a lower bound much closer than that: a wrong, shifted or turned strut or a misplaced hub breaks these, as the review's mutations showed); each master strut's long-point length measured and in one piece (its faces counted, see F-068); the longest strut in stock length and within slenderness 180 about the thin axis, the shortest not stubbier than 6 × its depth; sound timber between the two fins of the shortest strut; bolt spacing, edge distance and cheek thickness measured on the master strut, the bolt holes through; the fin inside the strut depth; the fin holes at least the plate thickness; the cut sheet and the templates holding the right parts; struts and hubs above the ring, and each seat post stopping 0.5 to 3 mm under its tube; at the tightest hub of each frequency two struts measured clear of each other and the two closest fins with at least 15 mm of weld access.

tools/jigs.py check runs check-range: 106 points (the defaults, the corners of the ranges, every choice and 32 random points from seed 1), all passing, none unproven. By hand, with param.set, the ends of the radius range were tried for every dome and strut section, the ends of the floor-area range for three of those, and the combinations that must be refused: the form refuses a 1V dome of 2.2 m and a 3V dome of 4.9 m from 38 x 89 mm timber (slenderness), and a 8 mm plate on a 38 mm strut. What this does not prove: the structural strength of the dome under load (the limits are proportion rules: slenderness 180 is the limit of BS 5268-2:2002, a code since withdrawn, cited through RoyMech, and EN 1995-1-1 gives no such limit; the rest are this Jig's own rules; none of them is a calculation; have a structure of this size checked by an engineer). The clash and weld checks measure the tightest pair per frequency, not every pair.

Export

• Laser: File › Export, Sheet of set: Hub plates to laser cut, DXF or SVG: one fin plate per strut type, one hub cap plate and one anchor plate, each on its layer. The outputs say how many of each to cut (fins: two per strut of that type).
• Strut templates: Sheet of set: Strut templates, DXF or SVG: each strut type's wide face between the short points of its mitres with its four bolt holes, true size, for marking out (the mitre angle and the kerf are outputs).
• Saw list: the outputs (count and length of each type). cut.list, with the bodies Fin A, Fin B, Fin C and Hub cap plate, lists the plates at the 3V defaults. At 1V or 2V the named set is the one to export, because a body list naming an inactive fin fails (J-003).

The README in the model's repository has the rest (Files, Rebuild, Difficulty, Platform notes, Licence): the whole README on GitHub.