Geodesic dome and polyhedron calculator

Pick a frequency and a size and it lists everything you need to build the frame: how many struts of each length, what meets at each hub, the angles to bend or cut, and how to get the struts out of your stock with the least waste. Panels come out as real-size templates.

How to use it

Frequency 1V to 6V: the higher, the rounder and the more (shorter) struts.
Truncation: the whole sphere, or a dome cut through a ring of hubs. The named ones are the usual builds — 2V, 4V and 6V halves, 3V 3/8 and 5/8. Odd frequencies have no level ring: the base hubs differ a little in height (the tool says how much). Flatten the base drops them straight down onto one plane, which gives the bottom struts a few new lengths.
Radius (or diameter) of the sphere through the hub centres.
Struts: chord factor × radius is hub centre to hub centre. Each end ± adjusts the cut length — take off a hub’s radius, or add the length for flattened, drilled conduit ends. With your stock length, saw kerf and a few spares, the cut list packs the struts into bars (first fit decreasing) and shows each bar pattern.
Hubs are grouped by the order of strut types round them, with the angles between neighbours seen from outside. End angle is how far each strut dips below the hub’s tangent plane — the bend for flattened conduit, or the angle of a hub plate. Dihedral is the angle between the two panels on a strut.
Panels: one template per triangle type, hub centre to hub centre, with a seam allowance for a fabric or film cover, or with the edge bevel for each side of a ply panel. Print them at real size: large panels are tiled over A4, Letter or A3 with an overlap, trim lines and a page map, and there is a 100 mm square to check the scale. SVG and DXF are true size in millimetres.

The Polyhedra tab does the five Platonic solids and the truncated icosahedron (a football) for lamp shades and models: face templates with glue tabs and fold lines, an extra face with a hole for the lamp holder, and the dihedral angles (and the edge bevel for solid panels).

For timber, the cut list tool packs sheet goods and boards; the lumber calculator prices them; the beams and trusses solver checks members; and laser-cut patterns does finger-jointed hub plates.

How it works

The icosahedron stands on its head with a vertex at the zenith. Each face is split into ν² small triangles and every new point is pushed out onto the sphere (class I, the method in most dome tables), so chord factors are just lengths on a unit sphere: 2V gives A = 0.54653 and B = 0.61803, 3V gives 0.34862, 0.40355 and 0.41241. Struts are lettered by length, shortest first. The 3-D view (three.js) colours struts by type.

Browser support

Any current browser. The 3-D preview needs WebGL; printing uses the browser’s print dialog.

Privacy

All the arithmetic happens in your browser, and your settings stay in its local storage. The page loads three.js (the 3-D view) and, when you download a PDF, jsPDF, from cdn.jsdelivr.net.