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Figure 1. Illustration of a dodecahedron built with double-ended magnets (unit of five), which assembled with two vertices having all one pole (near and far vertices in red), and alternating vertices of two blue and a red, or two red and a blue.
Figure 2. A dodecahedron after compressing Phi to one.

The dodecahedron is one of the regular polyhedra in the family of the five Platonic Solids.

The dodecahedron has vertices based on the natural constant, Phi (about 1.618). If Phi is arbitrarily warped, compressing it to the value of one (1), the image of Fig. 2 results as a cube seen through from an axis between corners. See Video 1 for an animated sequence of the expansion from a cube with faces divided into rectangles as it is inflated to a perfect dodecahedron.

Video 1. Warping a bifurcated cube into a dodecahedron. Also notice in Video 1 how there is a rotation of the corner edges about the eight corners of the cube. More to come.  —DEM