K4.8 dual (EntityTopic, 10)
From Hi.gher. Space
(Difference between revisions)
m (not a segmentochoron) |
(polytope explorer integration) |
||
| (2 intermediate revisions not shown) | |||
| Line 1: | Line 1: | ||
| - | <[#ontology [kind topic] [cats 4D]]> | + | <[#ontology [kind topic] [cats 4D Polytope]]> |
{{STS Shape | {{STS Shape | ||
| - | | image=<[# | + | | image=<[#embed [hash T5ERME8F013WMG88YCN4WSFM1J]]><br />[[Petrie polygon]] |
| dim=4 | | dim=4 | ||
| elements=8, 18, 17, 7 | | elements=8, 18, 17, 7 | ||
| Line 9: | Line 9: | ||
| dual=[[K4.8]] | | dual=[[K4.8]] | ||
}}}} | }}}} | ||
| - | |||
The '''K4.8 dual''' is currently unnamed. Its cells are 4 [[tetrahedra]] and 4 [[square pyramid]]s. Its faces are 2 [[square]]s and 4+4+8 [[triangle]]s. It has 1+4+4+4+4 edges and 1+2+4 vertices. | The '''K4.8 dual''' is currently unnamed. Its cells are 4 [[tetrahedra]] and 4 [[square pyramid]]s. Its faces are 2 [[square]]s and 4+4+8 [[triangle]]s. It has 1+4+4+4+4 edges and 1+2+4 vertices. | ||
== Structure == | == Structure == | ||
| - | |||
{| style='text-align: center;' | {| style='text-align: center;' | ||
| - | |<[# | + | |<[#embed [hash YYZSJCPVP554RMJ8AFHMYNS40J]]><br/>Two of four tetrahedrons highlighted |
| - | |<[# | + | |<[#embed [hash K4A3JXPP3050YT86PT7ER5VQYF]]><br/>The other two tetrahedrons highlighted |
|- | |- | ||
| - | |style='width: 300px;'|<[# | + | |style='width: 300px;'|<[#embed [hash KC5ZTY08P2ZAMBJR0CWMR3NHXX]]><br/>Two of four square pyramids highlighted.<br/>Their apexes are the leftmost and rightmost<br/>vertices and they meet at their bases |
| - | |style='width: 300px;'|<[# | + | |style='width: 300px;'|<[#embed [hash 24SHA3B0VQFSATFZ0SSMG3MBM9]]><br/>The other two square pyramids highlighted.<br/>Their apexes are the topmost and bottommost<br/>vertices and they meet at their bases |
|} | |} | ||
| + | |||
| + | <[#polytope [id 61]]> | ||
Latest revision as of 22:36, 16 February 2014
The K4.8 dual is currently unnamed. Its cells are 4 tetrahedra and 4 square pyramids. Its faces are 2 squares and 4+4+8 triangles. It has 1+4+4+4+4 edges and 1+2+4 vertices.
Structure
 Two of four tetrahedrons highlighted |  The other two tetrahedrons highlighted |
 Two of four square pyramids highlighted. Their apexes are the leftmost and rightmost vertices and they meet at their bases |  The other two square pyramids highlighted. Their apexes are the topmost and bottommost vertices and they meet at their bases |
Incidence matrix
Dual: K4.8
| # | TXID | Va | Vb | Vc | Ea | Eb | Ec | Ed | Ee | 4a | 3a | 3b | 3c | C1a | C2a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | ||||||||||||||
| 1 | Vb | = point | ; | ||||||||||||||
| 2 | Vc | = point | ; | ||||||||||||||
| 3 | Ea | 0 | 1 | 1 | = digon | ; | |||||||||||
| 4 | Eb | 0 | 0 | 2 | = digon | ; | |||||||||||
| 5 | Ec | 1 | 1 | 0 | = digon | ; | |||||||||||
| 6 | Ed | 0 | 2 | 0 | = digon | ; | |||||||||||
| 7 | Ee | 0 | 1 | 1 | = digon | ; | |||||||||||
| 8 | 4a | 1 | 2 | 1 | 2 | 0 | 2 | 0 | 0 | = square | ; | ||||||
| 9 | 3a | 1 | 2 | 0 | 0 | 1 | 2 | 1 | 0 | = triangle | ; | ||||||
| 10 | 3b | 0 | 2 | 1 | 1 | 0 | 0 | 1 | 1 | = triangle | ; | ||||||
| 11 | 3c | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 1 | = triangle | ; | ||||||
| 12 | C1a | 1 | 3 | 1 | 2 | 0 | 3 | 2 | 1 | 1 | 2 | 2 | 0 | = square pyramid | ; | ||
| 13 | C2a | 0 | 2 | 2 | 2 | 1 | 0 | 1 | 2 | 0 | 0 | 2 | 2 | = tetrahedron | ; | ||
| 14 | H4.1a | 1 | 4 | 2 | 4 | 1 | 4 | 4 | 4 | 2 | 4 | 8 | 4 | 4 | 4 | = K4.8 dual | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
