Tetrakis hexahedron

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Tetrakis hexahedron
Tetrakis hexahedron
(Click here for rotating model)
Type Catalan solid
Face type isosceles triangle
Faces 24
Edges 36
Vertices 14
Vertices by type 6{4}+8{6}
Face configuration V4.6.6
Symmetry group Oh, [4,3], *432
Dihedral angle 143°7'48"
 \arccos ( -\frac{4}{5} )
Properties convex, face-transitive
Truncated octahedron.png
Truncated octahedron
(dual polyhedron)
Tetrakis hexahedron Net
Net

In geometry, a tetrakis hexahedron (also known as a tetrahexahedron) is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid. It can be seen as a cube with square pyramids covering each square face; that is, it is the Kleetope of the cube.

It also can be called a disdyakis hexahedron as the dual of an omnitruncated tetrahedron.

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Naturally occurring (crystal) formations of tetrahexahedra are observed in copper and fluorite systems.

Polyhedral dice shaped like the tetrakis hexahedron are occasionally used by gamers.

A 24-cell viewed under a vertex-first perspective projection has a surface topology of a tetrakis hexahedron and the geometric proportions of the rhombic dodecahedron, with the rhombic faces divided into two triangles.

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