Snub disphenoid (EntityTopic, 14)
From Hi.gher. Space
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''See also:'' [[Derivation of snub disphenoid coordinates]] | ''See also:'' [[Derivation of snub disphenoid coordinates]] | ||
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Revision as of 04:32, 15 March 2016
The snub disphenoid is the 84th Johnson solid, J84.
Cartesian coordinates
The Cartesian coordinates of the snub disphenoid, centered on the origin and with edge length 2, are:
- (0, A, ±1)
- (±C, B, 0)
- (0, -B, ±C)
- (±1, -A, 0)
where A=√u, B=√v, C=√w, and u, v, w are roots of the following cubic polynomials:
- 2u3 + 11u2 + 4u - 1 = 0, 2 < u < 3;
- v3 - 17v2 + 64v - 64 = 0, 0 < v < 1;
- 2w3 - w2 - 8w - 4 = 0, 1 < w < 2.
See also: Derivation of snub disphenoid coordinates
Images
Incidence matrix
Dual: digon-unpinched pentagonal prism
| # | TXID | Va | Vb | Ea | Eb | Ec | Ed | 3a | 3b | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | ||||||||
| 1 | Vb | = point | ; | ||||||||
| 2 | Ea | 2 | 0 | = digon | ; | ||||||
| 3 | Eb | 1 | 1 | = digon | ; | ||||||
| 4 | Ec | 1 | 1 | = digon | ; | ||||||
| 5 | Ed | 0 | 2 | = digon | ; | ||||||
| 6 | 3a | 2 | 1 | 1 | 1 | 1 | 0 | = triangle | ; | ||
| 7 | 3b | 1 | 2 | 0 | 0 | 2 | 1 | = triangle | ; | ||
| 8 | C1a | 4 | 4 | 4 | 4 | 8 | 2 | 8 | 4 | = snub disphenoid | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
