Digonal gyrobicupolic ring (EntityTopic, 17)
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| - | The '''digonal gyrobicupolic ring''' is a | + | The '''digonal gyrobicupolic ring''', or '''K4.8''', is a member of the set of [[bicupolic ring]]s. Its cells are 1 [[tetrahedron]], 4 [[square pyramid]]s and 2 [[triangular prism]]s. Its faces are 1+4 [[square]]s and 4+4+4 [[triangle]]s. It has 2+4+4+8 edges and 4+4 vertices. |
[[Keiji]] studied it explicitly to try to understand more about the segmentochora. | [[Keiji]] studied it explicitly to try to understand more about the segmentochora. | ||
Revision as of 12:37, 8 February 2014
The digonal gyrobicupolic ring, or K4.8, is a member of the set of bicupolic rings. 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| ExPar: [#img] is obsolete, use [#embed] instead Petrie polygon | ExPar: [#img] is obsolete, use [#embed] instead Square pyramid and opposite triangle highlighted | ExPar: [#img] is obsolete, use [#embed] instead Tetrahedron and opposite square highlighted | ExPar: [#img] is obsolete, use [#embed] instead Triangular prism and opposite digon highlighted |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- ExPar: [#img] is obsolete, use [#embed] instead
