Platonic Solid Study #4: Dodecahedron

Understanding the geometry of dodecahedron.  A dodecahedron is formed by 12 identical faces of regular pentagons.

The geometry is created with 3 parts:  the top and the bottom are two identical pentagonal frustums, one rotated at 36 degrees to the other.  Each frustum is created by blending two pentagons.

The middle part is a blend of two pentagons, one rotated at 36 degrees to the other.

While blending the two pentagons, warp surfaces will be created instead of flat ones.  Adding an edge between two vertice will turn a warp surface into two flat surfaces.

Parameters and Math

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