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 inverse of the Vector Equilibrium (cubooctahedron), a form of great importance to Buckminster Fuller.
In terms of sacred geometry, this form is a transition to the dodecahedron and icoshedron. 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?
Here are 2 QTVRs. 1. Haptihedron outline with three sets of opposing faces: red, yellow, and blue. These faces show the expanded cube. (That is the one on this page.) 2. Haptihedron with a circle ringing each side of a set of opposing faces: rings of orange, green, and purple. The cube has 3 circles. The haptihedron has 6 circles.