Snub disphenoid (EntityTopic, 14)
From Hi.gher. Space
(Difference between revisions)
(stub) |
(→Cartesian coordinates: Ugh, the equations were transposed) |
||
(9 intermediate revisions not shown) | |||
Line 1: | Line 1: | ||
<[#ontology [kind topic] [cats 3D Crown_jewel] [alt [[freebase:0494gc]] [[wikipedia:Snub_disphenoid]]]]> | <[#ontology [kind topic] [cats 3D Crown_jewel] [alt [[freebase:0494gc]] [[wikipedia:Snub_disphenoid]]]]> | ||
{{STS Shape | {{STS Shape | ||
+ | | image=<[#embed [hash A267YZ2WP5WSTZ5CB56YGYETSJ]]> | ||
| dim=3 | | dim=3 | ||
| elements=12, 18, 8 | | elements=12, 18, 8 | ||
| sym=[[Biantiprismatic symmetry|D<sub>2d</sub>]] | | sym=[[Biantiprismatic symmetry|D<sub>2d</sub>]] | ||
| extra={{STS Polytope | | extra={{STS Polytope | ||
+ | | dual=[[Digon-unpinched pentagonal prism]] | ||
}}}} | }}}} | ||
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: | ||
+ | |||
+ | :<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]] | ||
+ | |||
+ | == 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 |