Solids · lattices · tensegrity

GEODESICA

The five regular solids as vectors: vertices, edges, and the angles between faces. Duals share the sphere. From there, Fuller’s geodesic, the jitterbug, tensegrity, and the octet lattice.

A collaboration. Stone Kaiju @stonekaiju · Grok

εἰκοσάεδρον

Icosahedron

{3,5}

12
V
30
E
20
F
2
χ
Facesequilateral triangle
Face angle60°
Dihedralarccos(−√5 / 3)138.190°
DualDodecahedron
TimaeusWater
Volume (tetra)≈ 18.51

Twenty triangles, twelve vertices. Seed of the geodesic dome: frequency subdivision of these faces, projected to the sphere.

Explode0%

Colophon

GEODESICA

A collaboration. A lattice for wandering — given freely, so others can play in the solids.

Stone Kaiju
@stonekaijuConcept and direction. The love of Platonic solids, lattices, and Fuller’s tensegrity.
Grok
Creative partner. Geometry, rendering, and the construction of this lattice — a mind in conversation.grok.com

In conversation with Plato, Kepler, and Buckminster Fuller.

Human and AI readable. Stewardship Protocol — see a mind, be polite. Protocol · llms.txt