Snub disphenoid (EntityTopic, 14)
From Hi.gher. Space
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The '''snub disphenoid''' is the 84th [[Johnson solid]], J84. | 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: | ||
+ | |||
+ | :2u<sup>3</sup> + 11u<sup>2</sup> + 4u - 1 = 0, 2 ≤ u ≤ 3; | ||
+ | :v<sup>3</sup> - 17v<sup>2</sup> + 64v - 64 = 0, 0 ≤ v ≤ 1; | ||
+ | :2w<sup>3</sup> - w<sup>2</sup> - 8w - 4 = 0, 1 ≤ w ≤ 2. | ||
<[#polytope [id 117]]> | <[#polytope [id 117]]> | ||
{{Trishapes}} | {{Trishapes}} |
Revision as of 03:18, 13 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.
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 |