Imagine, Geometry - haptihedron

These pages are to give flight to your imagination.

haptihedron Two tetrahedrons form a cube. The cube expands into a haptihedron. Sometimes I call it a movey. These are my pet names for the uniform polyhedron technically called a rhombicuboctahedron. This is a form I envisioned and investigated intensively. (See the story in Light Body.) So far, I haven't found references to it elsewhere. It is the visual inverse of the Vector Equilibrium (cuboctahedron), a form of great importance to Buckminster Fuller. The vertices of one are centered in the faces of the other.

In terms of sacred geometry, this form is a transition to the dodecahedron and icosahedron. I'm focused on details of the transition. How can I picture the change? The haptihedron has six great circles arranged orthogonally around the three dimensions of a cube. That is x, y, and z axes or horizontal, vertical, and depth oriented. What makes one circle migrate to make a form with six axes? How does the process of change look from the inside?

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