Tetrakis hexahedron
From Wikipedia, the free encyclopedia
| 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 or *432 |
| Dihedral angle | 143°7'48" |
| Properties | convex, face-transitive |
 Truncated octahedron (dual polyhedron) |
 Net |
A tetrakis hexahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated octahedron. It can be seen as a cube with square pyramids covering each square face.
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[edit] Uses
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.[citation needed]
[edit] See also
[edit] References
- 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)
[edit] External links
- Eric W. Weisstein, Tetrakis hexahedron (Catalan solid) at MathWorld.
- Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
- VRML model
- Conway Notation for Polyhedra Try: "dtO"
- Tetrakis Hexahedron -- Interactive Polyhedron model
- The Uniform Polyhedra
