K4.8 dual (EntityTopic, 10)
From Hi.gher. Space
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.
