Digonal gyrobicupolic ring (EntityTopic, 17)
From Hi.gher. Space
K4.8 is the first as-yet-unclassified convex segmentochoron. Its cells are 1 tetrahedron, 4 square pyramids and 2 triangular prisms. Its faces are 1+4 squares and 4+4+4 triangles. It has 2+4+4+8 edges and 4+4 vertices.
Keiji studied it explicitly to try to understand more about the segmentochora.
Construction
It is possible to construct K4.8 from three different pairs of polytopes:
| ExPar: [#img] is obsolete, use [#embed] instead Square pyramid and opposite triangle highlighted | ExPar: [#img] is obsolete, use [#embed] instead Tetrahedron and opposite square highlighted | ExPar: [#img] is obsolete, use [#embed] instead Triangular prism and opposite digon highlighted |
This segmentochoron also arises from a bidiminishing of the rectified 5-cell. First, delete any vertex from the rectified 5-cell. That forms the monodiminished rectified 5-cell, in which there are 1 triangular prism, 2 octahedra, 3 square pyramids, and 3 tetrahedra (same as the segmentochoron trigonal_prism||gyrated_triangle). If a vertex from the gyrated triangle is deleted, it will create a second triangular prism, thus resulting in this segmentochoron.
