Tetrakis hexahedron

Tetrakis hexahedron
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

In geometry, a tetrakis hexahedron 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.



Naturally occurring (crystal) formations of tetrahexahedrons 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.


See also


  • Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.  (Section 3-9)
  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR730208  (The thirteen semiregular convex polyhedra and their duals, Page 14, Tetrakishexahedron)
  • The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ISBN 978-1-56881-220-5 [1] (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 284, Tetrakis hexahedron )

External links