Digonal gyrobicupolic ring (EntityTopic, 17)
From Hi.gher. Space
(construction as a bidiminishing of the rectified 5-cell) |
(rectified is ambiguous; name and index for the monodiminished polychoron) |
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| - | This segmentochoron also arises from a bidiminishing of the | + | |
| + | This segmentochoron also arises from a bidiminishing of the [[3-pyrotomochoron]]. First, delete any vertex from the 3-pyrotomochoron. That forms the ''(mono)diminished 3-pyrotomochoron'', better known as the [[trigonal biantiprismatic ring]], or ''K4.6''; its cells are 1 triangular prism, 2 [[octahedra]], 3 square pyramids, and 3 tetrahedra. It can be constructed as ''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. | ||
Revision as of 18:43, 27 August 2012
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| ExPar: [#img] is obsolete, use [#embed] instead Square pyramid and opposite triangle highlighted | ExPar: [#img] is obsolete, use [#embed] instead Tetrahedron and opposite square highlighted | ExPar: [#img] is obsolete, use [#embed] instead Triangular prism and opposite digon highlighted |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 3-pyrotomochoron. First, delete any vertex from the 3-pyrotomochoron. That forms the (mono)diminished 3-pyrotomochoron, better known as the trigonal biantiprismatic ring, or K4.6; its cells are 1 triangular prism, 2 octahedra, 3 square pyramids, and 3 tetrahedra. It can be constructed as 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.
