Snub disphenoid (EntityTopic, 14)
From Hi.gher. Space
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where A=√u, B=√v, C=√w, and u, v, w are roots of the following cubic polynomials: | where A=√u, B=√v, C=√w, and u, v, w are roots of the following cubic polynomials: | ||
| - | :2u<sup>3</sup> | + | :<table><tr><td style="vertical-align:bottom">2u<sup>3</sup> - u<sup>2</sup> - 8u - 4 = 0</td><td style="padding-left:2em; vertical-align:bottom">2 < u < 3</td></tr><tr><td style="vertical-align:bottom">2v<sup>3</sup> + 11v<sup>2</sup> + 4v - 1 = 0</td><td style="padding-left:2em; vertical-align:bottom">0 < v < 1</td></tr><tr><td style="vertical-align:bottom">w<sup>3</sup> - 17w<sup>2</sup> + 64w - 64 = 0</td><td style="padding-left:2em; vertical-align:bottom">1 < w < 2</td></tr></table> |
| - | : | + | |
| - | : | + | The values of A, B, C are approximately: |
| + | :A = 1.567861848465127 | ||
| + | :B = 0.411123131706519 | ||
| + | :C = 1.289168546448310 | ||
''See also:'' [[Derivation of snub disphenoid coordinates]] | ''See also:'' [[Derivation of snub disphenoid coordinates]] | ||
| + | |||
| + | == Images == | ||
| + | |||
| + | <[#embed [hash PG0H4HNDJS6HPN2NXXR3JVWSNK]]> | ||
| + | |||
| + | == Software models == | ||
| + | |||
| + | *[[Stella4d]] [http://hi.gher.space/dl/BAPERT6G5TVJAGTEP994W1AXFS.off .off file] | ||
| + | *[[Polyview]] [http://hi.gher.space/dl/5DJKMTDVYT3WWG4FPX6TPRTCG0.def .def file] | ||
<[#polytope [id 117]]> | <[#polytope [id 117]]> | ||
{{Trishapes}} | {{Trishapes}} | ||
Latest revision as of 22:20, 14 July 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 - u2 - 8u - 4 = 0 2 < u < 3 2v3 + 11v2 + 4v - 1 = 0 0 < v < 1 w3 - 17w2 + 64w - 64 = 0 1 < w < 2
The values of A, B, C are approximately:
- A = 1.567861848465127
- B = 0.411123131706519
- C = 1.289168546448310
See also: Derivation of snub disphenoid coordinates
Images
Software models
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 |
