| Tetrakis hexahedron | |
|---|---|
 (Click here for rotating model) | |
| Type | Catalan solid |
| Coxeter diagram |    
|
| Conway notation | kC |
| Face type | V4.6.6 isosceles triangle |
| Faces | 24 |
| Edges | 36 |
| Vertices | 14 |
| Vertices by type | 6{4}+8{6} |
| Symmetry group | Oh, B3, [4,3], (*432) |
| Rotation group | O, [4,3]+, (432) |
| Dihedral angle | 143°07′48″ arccos(−4/5) |
| Properties | convex, face-transitive |
 Truncated octahedron (dual polyhedron) |
 Net |
Dual compound of truncated octahedron and tetrakis hexahedron. The woodcut on the left is from Perspectiva Corporum Regularium (1568) by Wenzel Jamnitzer.
Die and crystal model
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Drawing and crystal model of variant with tetrahedral symmetry called hexakis tetrahedron [1]
In geometry, a tetrakis hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube[2]) is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid.
It can be called a disdyakis hexahedron or hexakis tetrahedron as the dual of an omnitruncated tetrahedron, and as the barycentric subdivision of a tetrahedron.[3]
- ^ Hexakistetraeder in German, see e.g. Meyers page and Brockhaus page. The same drawing appears in Brockhaus and Efron as преломленный пирамидальный тетраэдр (refracted pyramidal tetrahedron).
- ^ Conway, Symmetries of Things, p.284
- ^ Langer, Joel C.; Singer, David A. (2010), "Reflections on the lemniscate of Bernoulli: the forty-eight faces of a mathematical gem", Milan Journal of Mathematics, 78 (2): 643–682, doi:10.1007/s00032-010-0124-5, MR 2781856
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