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 |
![](http://upload.wikimedia.org/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] and has a shäfli symbol of tr{4,3/2}
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 |
![](http://upload.wikimedia.org/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.
Proportions
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. Archived from the original on 2015-03-29.
- 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