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Geodesic Math and How to Use It

A technical manual for calculating geodesic and tensegrity structures — shell-like forms that hold themselves up without supporting columns by exploiting a three-way grid of tensile forces. It works through weight-versus-tension, tensegrity prisms, spherical tensegrities, equilibrium, and elasticity multiplication.

Updated 2026-06-27 medium confidence cold

Geodesic Math and How to Use It

Geodesics is a technique for making shell-like structures that hold themselves up without supporting columns, by exploiting a three-way grid of tensile forces. They are very strong and can be very large — the geodesic bubble built for the United States exhibits at Expo '67 in Montréal encloses some 6 million cubic feet, roughly three-fourths of a sphere 250 feet in diameter, yet weighs only about 600 tons. Despite their potential, in the quarter-century since Fuller introduced them they had not been used widely.

Core structure

  • What This Book Is
  • Weight vs. Tension
  • Appendix to Chapter 1: Tensegrity Prisms
  • Spherical Tensegrities
  • Equilibrium
  • Elasticity Multiplication

Main ideas

  • Geodesics make shell-like structures that stand without columns by exploiting a three-way grid of tensile forces.
  • Conventional structure relies on beams supported by posts; geodesic/tensegrity structure replaces this with distributed tension.
  • The simplest tensegrity (Diagram 1.5) consists of 3 compressive struts and 9 tensile tendons (a tendon being the portion of the tensile network between two adjacent strut ends).
  • The three-strut tensegrity of Chapter 1 is asymmetrical, with triangular ends and rhomboidal sides.
  • When the tension members of a tensegrity are taut, the structure is in a state of equilibrium.

Why it matters

The book turns Fuller's geometric intuitions into usable engineering mathematics, giving builders the equations behind geodesic domes and tensegrity structures. Its illustrations — from the Montréal Expo bubble to the thought-experiment of a half-mile sphere that would float on a one-degree temperature difference — make the extraordinary strength-to-weight ratios of these forms concrete.

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