Snub disphenoid (EntityTopic, 14)
From Hi.gher. Space
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.
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 |
