Square biantiprismatic ring (EntityTopic, 19)
From Hi.gher. Space
The square biantiprismic ring is a member of the infinite family of biantiprismatic rings, which are 4D CRF polychora. It consists of a 3-membered ring containing two square antiprisms and a cube, flanked by a circle of 4 tetrahedra and 4 square pyramids.
Cartesian coordinates
Cube:
(±1, ±1, ±1, 0)
Square:
(±√2, 0, 0, H) (0, ±√2, 0, H)
where H = √(2√2 - 1).
Incidence matrix
Dual: (dual of square biantiprismatic ring)
# | TXID | Va | Vb | Ea | Eb | Ec | Ed | 4a | 4b | 3a | 3b | 3c | 4c | C1a | C2a | C3a | C4a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; end | ||||||||||||||||
1 | Vb | = point | ; mid | ||||||||||||||||
2 | Ea | 2 | 0 | = digon | ; end | ||||||||||||||
3 | Eb | 2 | 0 | = digon | ; side | ||||||||||||||
4 | Ec | 1 | 1 | = digon | ; lace | ||||||||||||||
5 | Ed | 0 | 2 | = digon | ; mid | ||||||||||||||
6 | 4a | 4 | 0 | 4 | 0 | 0 | 0 | = square | ; end | ||||||||||
7 | 4b | 4 | 0 | 2 | 2 | 0 | 0 | = square | ; side | ||||||||||
8 | 3a | 2 | 1 | 1 | 0 | 2 | 0 | = triangle | ; lace end | ||||||||||
9 | 3b | 2 | 1 | 0 | 1 | 2 | 0 | = triangle | ; lace side | ||||||||||
10 | 3c | 1 | 2 | 0 | 0 | 2 | 1 | = triangle | ; lace mid | ||||||||||
11 | 4c | 0 | 4 | 0 | 0 | 0 | 4 | = square | ; mid | ||||||||||
12 | C1a | 4 | 4 | 4 | 0 | 8 | 4 | 1 | 0 | 4 | 0 | 4 | 1 | = square antiprism | ; | ||||
13 | C2a | 8 | 0 | 8 | 4 | 0 | 0 | 2 | 4 | 0 | 0 | 0 | 0 | = cube | ; | ||||
14 | C3a | 4 | 1 | 2 | 2 | 4 | 0 | 0 | 1 | 2 | 2 | 0 | 0 | = square pyramid | ; | ||||
15 | C4a | 2 | 2 | 0 | 1 | 4 | 1 | 0 | 0 | 0 | 2 | 2 | 0 | = tetrahedron | ; | ||||
16 | H4.1a | 8 | 4 | 8 | 4 | 16 | 4 | 2 | 4 | 8 | 8 | 8 | 1 | 2 | 1 | 4 | 4 | = square biantiprismatic ring | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
Additional images
Software models
ExPar [#models]: Unable to contact the polyview server at this time. Please try again later.