Platonic Solid Study #3: Icosahedron

Understanding the geometry of icosaahedron.  An icosahedron is formed by 20 identical faces of equilateral triangle.

The geometry is composed of 3 parts.  The middle part is a blend of two pentagons, one rotated at 45 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.

The top and the base parts are two pentagonal pyramids.  Each is created with an extrusion from a pentagon cut by a void sweep from the pentagon path with a triangle profile.

Parameters and Math

ICOSAHEDRON4

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