Hexagonal dome Pro

How it goes together

It is the football. The truncated icosahedron comes from slicing a pyramid off every vertex of an icosahedron, exactly one third of the way along each edge: each vertex leaves a pentagon — it had five edges — and each face, a triangle with its three points cut off, becomes a hexagon. Twelve and twenty, thirty-two faces in all.

One third is not a rough figure. It is the only fraction that makes the hexagon’s side come out equal to the pentagon’s, and that is the best thing about this solid: all ninety edges are exactly the same length. There is no “short strut and long strut” as in a geodesic dome.

And the sixty vertices land on a sphere by themselves. A geodesic dome is an approximation — you subdivide each face and push every new vertex out to the sphere; this one is exact, an Archimedean solid. All thirty-two faces are flat and regular before anyone computes anything.

Two angles in the whole solid, which means two clips. Where a pentagon meets a hexagon the sphere folds 138°, and between two hexagons, 142.5°. That is all. A 3V geodesic needs three different clips and has edges of three lengths; here the whole sphere is built from two clip types and two pieces: a pentagon and a hexagon.

The clip is what rules. It crosses the panel halfway — the web passes through the notch in the edge and the wings grip it on both faces — and carries the angle already drawn. Each panel ends up held on every side: to get out it would have to move away from one edge, which is exactly what the others prevent. It locks itself, with no glue or screws.

The top hole comes out whole, in one piece. There is a pentagon up there — not a hub, as in the geodesic dome, where the hole has to be shared out between the five panels that meet at the top — so the lamp-holder circle is cut complete in that one panel. 40 mm for a common E27, 30 for an E14. That panel comes out solid even if you ask for cut-out panels: between the cut-out and the hole there would be a loose ring of wood that drops off the sheet, and you want it solid right where the lamp is held anyway. If you hang it, use an LED.

The bottom row comes out trimmed flush with the floor. The cut snaps to the nearest ring of vertices so nothing comes off as a splinter, but when there is no ring nearby the plane cuts anyway and the bottom panels get a straight side with no notch on that edge. That is what makes the dome sit flat. One thing to watch: this solid has only eight rings of vertices — a 4V geodesic has far more — so there are few places to cut, and 5/8 can end up fairly close to the half sphere. The template says so when it happens.

There is a V between panels, on purpose. Two sheets cut square that meet at an angle dig into each other near the edge. Since the laser cannot bevel, every panel pulls back from the edge by whatever the angle asks for, and what you see is a V opening outwards instead of two edges overlapping. The clip takes up that gap: its web is those millimetres longer.

The clip is a press fit, and the kerf rules there. If it goes in loose, raise the kerf and cut another; if it will not go in, lower it. Cut one panel and one clip before you send the whole sheet.

You can engrave the name of every piece. Each panel comes out with its type engraved in the middle and, next to each notch, the number of the clip that goes there. There are fewer types here than in a geodesic dome, but the top pentagon and the pentagons below it are the same piece apart from the hole, so the label still saves a measurement.

The panels can be cut out. With the middle open it weighs less, uses less material and lets the light through. The cut-out suits this solid better than the geodesic one: a hollowed hexagon leaves an even six-sided border, and the whole thing reads as a honeycomb. The border has to be wider than the clip notch, or the cut-out eats the bottom of the notch.

A click in the 3D view pulls all the pieces apart and you can see how each clip goes into its notch. Another click puts it back.