A fabric or cable-net roof is stable only if it is prestressed into an anticlastic (saddle) shape, curved upward in one direction and downward in the other, so that wind from either side meets a surface already in tension.
Rules · Domes · Geometry · Structure
Enclose the most with the least: the geodesic dome
Frame a sphere by subdividing the triangular faces of an icosahedron and projecting the points onto the sphere; the triangulated net of short struts spreads loads through the whole surface and encloses the greatest volume for the least material.
full sphere of frequency ν: 30ν² struts, 20ν² triangles, 10ν² + 2 hubs
A sphere encloses more volume per unit of surface than any other shape, and a triangulated frame cannot change shape without changing the length of a member, so it is rigid with pin joints. The frequency (how many times each edge of the icosahedron is divided) sets the fineness of the net. A higher frequency gives shorter struts and a rounder dome, but more distinct strut lengths to fabricate; the counts shown in the figure are computed from the model itself.
Fuller’s own measure of success was weight: how many kilograms of structure per square metre of floor covered. His domes, delivered by helicopter or assembled by a few people from kits of struts, were among the lightest large enclosures ever built.
Related rules
Move ducts, pipes, lifts and escalators out of the building’s core onto its exterior, colour-code them, and let them become the architecture, leaving the interior free and making the plant easy to reach and replace.
Span the whole depth of the building with the structure so that each floor is a single open plate, adaptable to uses that cannot be foreseen.
Pompidou: 48 m clear span between column lines, 13 bays of 12.8 m
On an equator-facing window, make the overhang deep enough to shade the whole window from the high noon sun of summer, and no deeper, so that the low winter sun passes beneath it into the room.
noon sun altitude = 90° − latitude ± 23.44° · overhang D = window height ⁄ tan(summer altitude)
Hang the outer wall from the edges of the floor slabs as a continuous skin of glass and metal, independent of the frame behind it, and express its grid of mullions.
skin = vision glass + spandrel panel per floor, on a module of ≈ 1.5 m
Plan the permanent things (the structure, the service routes, the roads) as a lasting framework, and treat the enclosures plugged into it as a kit of standard parts, each renewed at its own rate.
Cite this page Chris Paton, “Enclose the most with the least: the geodesic dome”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/geodesic-efficiency. Text, drawings and models licensed under CC BY-NC 4.0.