The Cuboctahedron (green) within the Cube.

R. Buckminster Fuller called this the "Vector Equilibrium" or "VE"

because the radial distance from the center of volume to a vertex is the

same length as the distance from one surface vertex to a neighboring surface vertex.

This is a portion of a Face-centered Cubic (FCC) lattice.

Removing the square faces makes the Cuboctahedron flexible.

The flexing Cuboctahedron is called the "Jitterbug".

R. Buckminster Fuller knew (no reference on who discovered) that

during the Jitterbug flexing from the Cuboctahedron to the Octahedron

that it passes through positions corresponding to Icosahedra.

I (and others?) have discovered that the Jitterbug also passes through positions

corresponding to Dodecahedra which also correspond to Tetrahedra and Cubes.

**
All of the Platonic "solids" are encountered by the Jitterbug's dynamics.
**

Copyright September, 2007 by Robert W. Gray