Gyrated octahedral prism (EntityTopic, 14)
From Hi.gher. Space
The gyrated octahedral prism or K4.13 is a 4D analogue of the gyrobifastigium, J26.
Here is a render as seen from <5,0,0,0>:
Here is a render as seen from <0,5,0,0>:
Coordinates
<±1, ±1, 0, ±1> <0, 0, √2, ±1> <0, ±1, -√2, 0>
Incidence matrix
Dual: K4.13 dual
| # | TXID | Va | Vb | Ea | Eb | Ec | Ed | 3a | 3b | 4a | 4b | 4c | C1a | C2a | C2b | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; cube corners | ||||||||||||||
| 1 | Vb | = point | ; ends | ||||||||||||||
| 2 | Ea | 2 | 0 | = digon | ; around middle | ||||||||||||
| 3 | Eb | 2 | 0 | = digon | ; cube corners | ||||||||||||
| 4 | Ec | 1 | 1 | = digon | ; wall corners | ||||||||||||
| 5 | Ed | 0 | 2 | = digon | ; ends | ||||||||||||
| 6 | 3a | 2 | 1 | 0 | 1 | 2 | 0 | = triangle | ; wall corners | ||||||||
| 7 | 3b | 2 | 1 | 1 | 0 | 2 | 0 | = triangle | ; walls | ||||||||
| 8 | 4a | 4 | 0 | 4 | 0 | 0 | 0 | = square | ; in-out middle | ||||||||
| 9 | 4b | 4 | 0 | 2 | 2 | 0 | 0 | = square | ; around middle | ||||||||
| 10 | 4c | 2 | 2 | 1 | 0 | 2 | 1 | = square | ; walls | ||||||||
| 11 | C1a | 4 | 1 | 2 | 2 | 4 | 0 | 2 | 2 | 0 | 1 | 0 | = square pyramid | ; | |||
| 12 | C2a | 4 | 2 | 4 | 0 | 4 | 1 | 0 | 2 | 1 | 0 | 2 | = triangular prism | ; in-out | |||
| 13 | C2b | 4 | 2 | 2 | 2 | 4 | 1 | 2 | 0 | 0 | 1 | 2 | = triangular prism | ; walls | |||
| 14 | H4.1a | 8 | 4 | 8 | 4 | 16 | 2 | 8 | 8 | 2 | 4 | 8 | 4 | 4 | 4 | = gyrated octahedral prism | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
