Square biantiprismatic ring (EntityTopic, 19)
From Hi.gher. Space
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| - | The square biantiprismic ring is a member of the infinite family of [[ | + | <[#ontology [kind topic] [cats Uniform Prism Tapertope Biantiprismatic_ring]]> |
| - | + | {{STS Shape | |
| - | + | | image=<[#embed [hash DD3GJQSWCEV0G5C4NJJ0G4XFEW] [width 120]]> | |
| + | | dim=4 | ||
| + | | elements=11, 31, 32, 12 | ||
| + | | extra={{STS Polytope | ||
| + | }}}} | ||
| + | The '''square biantiprismic ring''' is a member of the infinite family of [[biantiprismatic ring]]s, 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 pyramid]]s. | ||
== Cartesian coordinates == | == Cartesian coordinates == | ||
| - | |||
Cube: | Cube: | ||
(±1, ±1, ±1, 0) | (±1, ±1, ±1, 0) | ||
Square: | Square: | ||
| - | ( | + | (±√2, 0, 0, H) |
| - | (0, | + | (0, ±√2, 0, H) |
| - | where H = | + | where H = √(2√2 - 1). |
| + | |||
| + | <[#polytope [id 95]]> | ||
| + | |||
| + | == Additional images == | ||
| + | <[#box [id 11] [width 150] [height 210]]> | ||
| + | |||
| + | == Software models == | ||
| + | <[#models [hash 0TJNTZ67SWCNAD20P82HYZ2BKE]]> | ||
Latest revision as of 23:09, 14 March 2014
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.
