Cubitruncated cuboctahedron
| Cubitruncated cuboctahedron | |
|---|---|
| File:Cubitruncated cuboctahedron.png | |
| 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 | Template:CDD |
| Wythoff symbol | |
| Symmetry group | Oh, [4,3], *432 |
| Index references | U16, C52, W79 |
| Dual polyhedron | Tetradyakis hexahedron |
| Vertex figure | File:Cubitruncated cuboctahedron vertfig.png 6.8.8/3 |
| Bowers acronym | Cotco |
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.
| File:Cubitruncated cuboctahedron convex hull.png Convex hull |
File:Cubitruncated cuboctahedron.png Cubitruncated cuboctahedron |
Orthogonal projection
File:Cubitruncated cuboctahedron ortho wireframes.png
Cartesian coordinates
Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of
- (±(Template:Radic−1), ±1, ±(Template:Radic+1))
Related polyhedra
Tetradyakis hexahedron
Template:Uniform dual polyhedron stat table
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
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External links
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- http://gratrix.net Uniform polyhedra and duals
- ↑ Script error: No such module "citation/CS1".