Digonal gyrobicupolic ring (EntityTopic, 17)
From Hi.gher. Space
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<[#ontology [kind topic] [cats 4D Bicupolic_ring Segmentochoron]]> | <[#ontology [kind topic] [cats 4D Bicupolic_ring Segmentochoron]]> | ||
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It is possible to construct the digonal gyrobicupolic ring from three different pairs of polytopes: | It is possible to construct the digonal gyrobicupolic ring from three different pairs of polytopes: | ||
{| style='text-align: center;' | {| style='text-align: center;' | ||
| + | |<[#img [hash DKVC00GZ95TX8Q6D2HCYGZ4EMJ]]><br/>[[Petrie polygon]]<br/> | ||
|<[#img [hash FQJDJCGRXBSBP94RHQHKJEA2MQ]]><br/>Square pyramid and<br/>opposite triangle highlighted | |<[#img [hash FQJDJCGRXBSBP94RHQHKJEA2MQ]]><br/>Square pyramid and<br/>opposite triangle highlighted | ||
|<[#img [hash E1T3GH5F04TPYTM0RR4485SQF4]]><br/>Tetrahedron and<br/>opposite square highlighted | |<[#img [hash E1T3GH5F04TPYTM0RR4485SQF4]]><br/>Tetrahedron and<br/>opposite square highlighted | ||
Revision as of 09:17, 8 February 2014
The digonal gyrobicupolic ring is a special member of the set of bicupolic rings. Unlike the others, only the gyro- form is possible, since ortho- or magna- forms would be degenerate. 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 the digonal gyrobicupolic ring from three different pairs of polytopes:
| ExPar: [#img] is obsolete, use [#embed] instead Petrie polygon | ExPar: [#img] is obsolete, use [#embed] instead Square pyramid and opposite triangle highlighted | ExPar: [#img] is obsolete, use [#embed] instead Tetrahedron and opposite square highlighted | ExPar: [#img] is obsolete, use [#embed] instead Triangular prism and opposite digon highlighted |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.
Projections
The following projection shows this segmentochoron from a viewpoint analogous to that of the other bicupolic rings, to show how the gyrated digons connect to each other via a tetrahedron (digon antiprism) and to the opposite square face via triangular prisms (digon cupolae).
- ExPar: [#img] is obsolete, use [#embed] instead
