4D Euclidean space

Polytope of the Month

This month, we introduce the castellated rhombicosidodecahedral prism:

The castellated rhombicosidodecahedral

Discovered in February 2014, this CRF polytope is the first known non-trivial polytope that contains bilunabirotundae as cells. In spite of the unusual shape of the bilunabirotunda, its deep connection with the icosahedron allows 30 copies of it to close up in 4D in icosahedral symmetry, resulting in a polytope with 30 biluna­birotundae sandwiched between two rhombicosi­dodecahedra, with the remaining gaps filled by 12 pentagonal pyramids and 20 tetrahedra.

This discovery led to a series of further discoveries in the same month of many related CRF polytopes that sport bilunabirotunda and triangular hebesphenorotunda cells, leading some of the members of the tetraspace forum to dub February 2014 as “CRFebruary”.

So, head on over to the castellated rhombicosidodecahedral prism page and learn all about this polytope that started it all! As usual, the full Cartesian coordinates are provided.


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Last updated 29 May 2014.

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