![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Cubohemioctahedron.png/640px-Cubohemioctahedron.png&w=640&q=50)
Cubohemioctahedron
Polyhedron with 10 faces / From Wikipedia, the free encyclopedia
In geometry, the cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15. It has 10 faces (6 squares and 4 regular hexagons), 24 edges and 12 vertices.[1] Its vertex figure is a crossed quadrilateral.
Cubohemioctahedron | |
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Type | Uniform star polyhedron |
Elements | F = 10, E = 24 V = 12 (χ = −2) |
Faces by sides | 6{4}+4{6} |
Coxeter diagram | ![]() ![]() ![]() ![]() |
Wythoff symbol | 4/3 4 | 3 (double-covering) |
Symmetry group | Oh, [4,3], *432 |
Index references | U15, C51, W78 |
Dual polyhedron | Hexahemioctacron |
Vertex figure | ![]() 4.6.4/3.6 |
Bowers acronym | Cho |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Cubohemioctahedron.stl/640px-Cubohemioctahedron.stl.png)
It is given Wythoff symbol 4⁄3 4 | 3, although that is a double-covering of this figure.
A nonconvex polyhedron has intersecting faces which do not represent new edges or faces. In the picture vertices are marked by golden spheres, and edges by silver cylinders.
It is a hemipolyhedron with 4 hexagonal faces passing through the model center. The hexagons intersect each other and so only triangular portions of each are visible.