4D Euclidean space
Polytope of the Month
This month, we introduce the castellated rhombicosidodecahedral prism:
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”.
29 May 2014:
Corrected numerous typos and other errors in several pages. Many thanks to John McIntosh for pointing them out!
2 May 2014:
The Polytope of the Month for May is up!
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