A geodesic dome encloses a lot of space with very little material, and it is built from a handful of repeated parts. That makes it a natural fit for sheet metal: a laser and a press brake can turn out dozens of identical struts or panels from a single flat pattern. The catch is that nothing in a dome is square. Every joint sits at a slight angle, the angles are not all the same, and small errors add up as you go round the structure.
This article covers the geometry you need to set out a dome, then looks at two ways to build one in sheet metal: formed struts with hubs, and flanged triangular panels that act as their own frame.
What a geodesic dome is
Start with an icosahedron: twenty equilateral triangles whose twelve corners all lie on a sphere. Divide each edge into equal parts, split each face into smaller triangles, and push the new points out onto the sphere. The number of divisions per edge is the frequency, written 1V, 2V, 3V and so on. Higher frequency means more, shorter struts and a smoother shape, but more joints.
Because the new points are pushed out to the sphere, the small triangles are no longer all equilateral, and the struts come in a few different lengths. Each length is expressed as a chord factor: the strut length for a sphere of radius 1. Multiply by the radius to the hub centres and you have the strut length.
Strut length L = CF × R
CF = 2 × sin(φ ÷ 2)R is the radius to the hub centres (or panel corners). φ is the angle the strut subtends at the centre of the sphere.
Chord factors for 2V and 3V
A 2V dome has just two strut lengths. The B struts are the halves of the original icosahedron edges, and their chord factor is exactly 1 ÷ φ (the golden ratio), 0.61803. The A struts run from the old corners to the new mid-edge points and are slightly shorter. With a five-way hub at the top, a 2V sphere cuts exactly at its equator, giving a hemisphere with a flat base.
| Frequency | Strut | Chord factor | Full sphere | Dome |
|---|---|---|---|---|
| 2V | A | 0.54653 | 60 | 30 (hemisphere) |
| 2V | B | 0.61803 | 60 | 35 (hemisphere) |
| 3V | A | 0.34862 | 60 | 30 (5/8 sphere) |
| 3V | B | 0.40355 | 90 | 55 (5/8 sphere) |
| 3V | C | 0.41241 | 120 | 80 (5/8 sphere) |
The 2V hemisphere has 65 struts, 26 hubs and 40 triangles: 30 isosceles A-A-B triangles and 10 equilateral B-B-B triangles. The hubs are 6 five-way, 10 six-way and 10 four-way at the base.
A worked example: 2V hemisphere, R = 3 m
- A = 0.54653 × 3000 = 1639.6 mm, 30 off
- B = 0.61803 × 3000 = 1854.1 mm, 35 off
- Total strut length = 30 × 1639.6 + 35 × 1854.1 = 114.1 m
- A-A-B panel: base 1854.1 mm, height √(1639.6² − 927.0²) = 1352.3 mm, area 1.25 m², 30 off
- B-B-B panel: side 1854.1 mm, height 1605.7 mm, area 1.49 m², 10 off
- Total panel area = 52.5 m², against 56.5 m² for the true hemisphere (2πR²)
These are node-to-node lengths. The cut length of a strut is shorter by whatever the hub takes up, and a panel built to these chords has its outside mould lines on the triangle edges. Decide early which surface the radius refers to, and write it on the drawing.
Option 1: formed struts and hubs
A strut can be a channel or hat section pressed from strip, with the web lying in the radial plane through the strut, and its end tabs bent to meet the hub. The angle between the strut axis and the plane tangent to the sphere at the hub is half the subtended angle:
θ = arcsin(CF ÷ 2)
A: θ = 15.86° B: θ = 18.00°For a 2V dome. A hub tab or flattened strut end is bent through this angle from the hub plane.
Sheet metal hubs work well: a laser-cut star plate with one tab per strut, each tab bent down by 15.9° or 18.0° depending on which strut lands on it. Five-way and six-way hubs need different blanks, and base hubs are half hubs welded or bolted to a ring beam. Mark the tab angle next to each tab on the flat pattern, because the two values are close enough to mix up on the shop floor.
Option 2: flanged panels as the frame
The more elegant route in sheet metal is to drop the struts altogether. Each triangle becomes a panel with a flange bent inwards along every edge. Neighbouring flanges are bolted back to back, and the flanges together form the frame. The skin and structure are one part, and there are only two panel types to make.
Dihedral angles and flange bends
For two flanges to bolt flat against each other, both must lie in the radial plane through the shared edge. That plane only bisects the joint when the two panels sit at the same distance from the centre. An A-A-B panel is slightly further out than a B-B-B panel, so along a B edge the two flanges are bent through different angles.
β = arcsin(d ÷ h)
d = √(R² − rc²) h = √(R² − (L ÷ 2)²)β is the angle between panel and flange. d is the distance from the dome centre to the panel plane, rc the panel circumradius, h the distance from the centre to the edge of length L.
| Edge | Panels either side | Panel to panel | Panel to flange | Bend-through angle |
|---|---|---|---|---|
| A | A-A-B / A-A-B | 157.54° | 78.77° each | 101.23° each |
| B | A-A-B / B-B-B | 161.97° | 82.78° / 79.19° | 97.22° / 100.81° |
The differences are only a few degrees, but bending every flange at an average value would leave the flanges gapping at one edge and forced together at the other. Set each bend in the model and let the CAD develop the flat pattern from your bend table; bends past 90° also need spring-back allowance, which the press brake operator will want to prove on a test piece.
Nesting and sheet size
Triangles nest well when alternate parts are rotated through 180°, so a strip of n triangles takes roughly (n + 1) × B ÷ 2 of sheet length. Flanges spoil perfect common-line cutting, so allow the flange width and a cutting gap on every slanted edge. Check the panel size against the sheet sizes your supplier actually stocks. In the example, the A-A-B panel is about 1.35 m high before flanges and fits a 3000 × 1500 mm sheet, but the B-B-B panel at 1.61 m does not. You would need a larger sheet, a split panel, a smaller radius or a higher frequency.
Keeping the water out
- Turn flanges inwards so the outside of every seam is a slight ridge that sheds water, never a gutter.
- Put gasket tape between flanges and cover each seam with a cap strip bedded on sealant. Fit caps from the base up so each upper cap laps over the one below.
- Cropped corners leave a small hole at every hub. Cover it with a hub cap, which can be a shallow pressed or bent disc.
- Use fasteners and sealants compatible with the panel material, and avoid mixing metals that will corrode each other.
- Detail the base ring with a drip so water runs off the dome, not into the foundation joint.
Tolerances add up
A dome closes on itself. Five panels meet at every five-way hub, and the base ring is ten B edges long, so small errors per part become visible gaps by the last panel. On a 40 mm flange, a 0.5° bend error moves the flange toe by 40 × tan(0.5°) ≈ 0.35 mm, so angle errors are usually forgiving. Hole position and edge length matter more. Laser-cut holes are typically very accurate, but bending moves them; a common approach is to make holes in one panel type slotted, or to drill one panel type on assembly. Confirm achievable tolerances with your fabricator before choosing.
Build a trial cluster before cutting the full set: one five-way hub with its five panels and one six-way hub will show up most setting-out errors.
Checklist
- Is the radius defined to hub centres, panel outer faces or flange faces, and is it on the drawing?
- Are the strut counts and lengths checked against the chord factor table for the chosen frequency and cut?
- Are flange bend angles set per edge and per panel type, not averaged?
- Do the panels, with flanges, fit a stocked sheet size?
- Is there a plan for seams, hub caps and the base drip?
- Have hole tolerances been agreed, and is a trial cluster planned?
If you would like a second pair of eyes on a dome, a faceted canopy or any panelised structure with awkward angles, send us your drawings.