Cubitruncated cuboctahedron: Difference between revisions
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{{Uniform polyhedra db|Uniform dual polyhedron stat table|ctCO}} |
{{Uniform polyhedra db|Uniform dual polyhedron stat table|ctCO}} |
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[[File:Tetradyakis hexahedron.stl|thumb|3D model of a tetradyakis hexahedron]] |
[[File:Tetradyakis hexahedron.stl|thumb|3D model of a tetradyakis hexahedron]] |
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The '''tetradyakis hexahedron''' (or '''great disdyakis dodecahedron''') is a nonconvex [[Isohedral figure|isohedral]] [[polyhedron]]. It has 48 intersecting [[scalene triangle]] faces, 72 edges, and 20 vertices. |
The '''tetradyakis hexahedron''' (or '''great disdyakis dodecahedron''') is a nonconvex [[Isohedral figure|isohedral]] [[polyhedron]]. It has 48 intersecting [[scalene triangle]] faces, 72 edges, and 20 vertices. The triangles have one angle of <math>\arccos(\frac{3}{4})\approx 41.409\,622\,109\,27^{\circ}</math>, one of <math>\arccos(\frac{1}{6}+\frac{7}{12}\sqrt{2})\approx 7.420\,694\,647\,42^{\circ}</math> and one of <math>\arccos(\frac{1}{6}-\frac{7}{12}\sqrt{2})\approx 131.169\,683\,243\,31^{\circ}</math>. The [[dihedral angle]] equals <math>\arccos(-\frac{5}{7})\approx 135.584\,691\,402\,81^{\circ}</math>. Part of each triangle lies within the solid, hence is invisible in solid models. |
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It is the [[Dual polyhedron|dual]] of the [[uniform star polyhedron|uniform]] cubitruncated cuboctahedron. |
It is the [[Dual polyhedron|dual]] of the [[uniform star polyhedron|uniform]] cubitruncated cuboctahedron. |
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== See also == |
== See also == |
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* [[List of uniform polyhedra]] |
* [[List of uniform polyhedra]] |
Revision as of 13:53, 2 July 2020
Cubitruncated cuboctahedron | |
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![]() | |
Type | Uniform star polyhedron |
Elements | F = 20, E = 72 V = 48 (χ = −4) |
Faces by sides | 8{6}+6{8}+6{8/3} |
Coxeter diagram | ![]() ![]() ![]() ![]() |
Wythoff symbol | 3 4 4/3 | |
Symmetry group | Oh, [4,3], *432 |
Index references | U16, C52, W79 |
Dual polyhedron | Tetradyakis hexahedron |
Vertex figure | ![]() 6.8.8/3 |
Bowers acronym | Cotco |
![](/upwiki/wikipedia/commons/thumb/f/f5/Cubitruncated_cuboctahedron.stl/220px-Cubitruncated_cuboctahedron.stl.png)
In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices.[1]
Convex hull
Its convex hull is a nonuniform truncated cuboctahedron.
![]() Convex hull |
![]() Cubitruncated cuboctahedron |
Orthogonal projection
Cartesian coordinates
Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of
- (±(√2−1), ±1, ±(√2+1))
Related polyhedra
Tetradyakis hexahedron
Tetradyakis hexahedron | |
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![]() | |
Type | Star polyhedron |
Face | ![]() |
Elements | F = 48, E = 72 V = 20 (χ = −4) |
Symmetry group | Oh, [4,3], *432 |
Index references | DU16 |
dual polyhedron | Cubitruncated cuboctahedron |
![](/upwiki/wikipedia/commons/thumb/b/b2/Tetradyakis_hexahedron.stl/220px-Tetradyakis_hexahedron.stl.png)
The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices. The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.
It is the dual of the uniform cubitruncated cuboctahedron.
See also
References
- ^ Maeder, Roman. "16: cubitruncated cuboctahedron". MathConsult.
{{cite web}}
: CS1 maint: url-status (link)
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208 p. 92
External links
- Weisstein, Eric W. "Cubitruncated cuboctahedron". MathWorld.
- Weisstein, Eric W. "Tetradyakis hexahedron". MathWorld.
- http://gratrix.net Uniform polyhedra and duals