Digonal gyrobicupolic ring (EntityTopic, 17)
From Hi.gher. Space
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| + | <[#ontology [kind topic] [cats 4D Segmentochoron]]> | ||
| + | {{STS Shape | ||
| + | | image=<[#img [hash DKVC00GZ95TX8Q6D2HCYGZ4EMJ]]><br />[[Petrie polygon]] | ||
| + | | dim=4 | ||
| + | | elements=7, 17, 18, 8 | ||
| + | | genus=0 | ||
| + | | extra={{STS Polytope | ||
| + | | petrie=8,0 | ||
| + | }}}} | ||
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'''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. | '''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. | ||
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It is possible to construct K4.8 from three different pairs of polytopes: | It is possible to construct K4.8 from three different pairs of polytopes: | ||
{| style='text-align: center;' | {| style='text-align: center;' | ||
| - | |||
|<[#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 | ||
|<[#img [hash 0NF1CPV2F19RM64G3F450VANMY]]><br/>[[Triangular prism]] and<br/>opposite [[digon]] highlighted | |<[#img [hash 0NF1CPV2F19RM64G3F450VANMY]]><br/>[[Triangular prism]] and<br/>opposite [[digon]] highlighted | ||
|} | |} | ||
Revision as of 14:25, 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.
Projections
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| ExPar: [#img] is obsolete, use [#embed] instead Square pyramid and opposite triangle highlighted | ExPar: [#img] is obsolete, use [#embed] instead Tetrahedron and opposite square highlighted | ExPar: [#img] is obsolete, use [#embed] instead Triangular prism and opposite digon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 |
