4D Euclidean space

News Archive

Apr 2018

This month we present a beautiful specimen of a CRF polytope that exemplifies the fascinating structure of the Hopf fibration of the 4D sphere. This structure is actually present in all of the regular polychora, but it is hidden within their higher degree of symmetry. In the swirl­prismato­diminished rectified 600-cell, however, this higher symmetry is stripped away, leaving bare the Hopf fibration substructure.

swirlprismatodiminished rectified 600-cell

Also known by its Bowers Acronym spidrox, this polychoron, in spite of being non-uniform because of its square pyramid cells, is nonetheless vertex-transitive and has equal edge lengths, and thus belongs to the class of scaliform polytopes. Its 600 square pyramids form 20 rings that wrap and twist around the 12 rings formed by its 120 pentagonal prisms and 120 pentagonal antiprisms, forming a marvelous 4D structure that corresponds with the discrete partitioning of the Hopf fibration according to the structure of the icosi­dodecahedron.

So head on over to the spidrox page to learn the structure of this beautiful polychoron. As usual, we provide the full coordinates.

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Last updated 26 Apr 2018.

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