Complexity of a Sphere.

Buckminster Fuller defines a Sphere (a) as “a multiplicity of discrete events, approximately equidistant in all directions from a Nuclear Center.”
The discrete points of such a System can be Inter-Triangulated.
The Tetrahedron (b), the Octahedron ©, and Icosahedron (d) are the only possible cases of Omni-Equilateral, Omni-Triangulated Finite Systems.
Pictured at (e) are the 15 great Circles developing from Rotation of the Icosahedron in respect to the 15 Axes Inter-Connecting opposite midpoints of the Icosahedron’s 30 edges. The 120 resulting right Spherical Triangles represent the maximum unitary subdivision of a One-Radius-System.