|Fig. 516.03 Frequency: A square of any frequency is
topologically equivalent to two adjacent triangles
corresponding frequency, i.e. a square has the same
number of vertexes as two adjacent triangles (A).
When the central sphere is removed from the vector equilibrium
(B), it contracts symmetrically to a more
compact arrangement (C), which is the icosahedron. The
vector equilibrium has eight triangular faces
and six square faces. The six square faces shift to
become 12 triangular faces: 12+8=20 triangular faces
of the icosahedron. Outer shells of the vector equilibrium
and icosahedron of the same frequency will
always have the same number of vertexes or spheres (D).
Therefore the equation 10F2 + 2 applies to
Copyright © 1997 Estate of R. Buckminster Fuller