4D Euclidean space

Polytope of the Month

This month, we introduce a simple but highly-interesting CRF polytope:


This is the projection of Cube atop Icosahedron, also known as K4.21, one of Dr. Klitzing's convex segmentochora. It is formed by placing an icosahedron and a cube in two parallel hyperplanes, and connecting them with 6 triangular prisms, 12 square pyramids, and 8 tetrahedra.

It is interesting because its two generating polyhedra come from two different symmetry groups, octahedral symmetry and icosahedral symmetry, unlike most of the other segmentochora where the two generating polyhedra come from the same family. Their common symmetry group is pyritohedral symmetry.

Find out more in the K4.21 page. As customary, we provide the full Cartesian coordinates.


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Last updated 01 Oct 2018.

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