Imagine, Geometry - haptihedron

These pages are to give flight to your imagination.

haptihedron vision of haptihedron descendingTwo 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 image to the left and story in Light Body.) So far, I haven't found references to it in this context elsewhere.

Here's what I wrote: "Funicula is initiated to the vision of the 'Haptihedron' by Amerindian guides. Her inner eye is opened. The octahedron inside the double tetrahedron of the Light Muscle appears expanded around her. Later, she realizes how the six sides of the cube are connected to the triangle corners to finish the shape." Note the figure in the middle.

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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