| Truncated Octahedron |
Article Index for Truncated |
Information AboutTruncated Octahedron |
| CATEGORIES ABOUT TRUNCATED OCTAHEDRON | |
| uniform polyhedra | |
| archimedean solids | |
| zonohedra | |
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The truncated octahedron is an Archimedean Solid . It has 8 regular hexagonal faces, 6 regular square faces, 24 vertices and 36 edges. Since each of its faces has Point Symmetry the truncated octahedron is a Zonohedron . __TOC__ COORDINATES AND PERMUTATIONS All Permutation s of (0, ±1, ±2) are Cartesian Coordinates of the Vertices of a Truncated Octahedron centered at the origin. The vertices are thus also the corners of 12 rectangles whose long edges are parallel to the coordinate axes. The truncated octahedron can also be represented by even more symmetric coordinates in four dimensions: all permutations of (1,2,3,4) form the vertices of a truncated octahedron in the three-dimensional subspace ''x'' + ''y'' + ''z'' + ''w'' = 10. For this reason the truncated octahedron is also sometimes known as the Permutohedron . AREA AND VOLUME The area ''A'' and the Volume ''V'' of a truncated octahedron of edge length ''a'' are: : : UNIFORM COLORINGS There are two Uniform Coloring s, with Tetrahedral Symmetry and Octahedral Symmetry : RELATED POLYHEDRA The truncated octahedron exists within the set of truncated forms between a Cube and Octahedron : TESSELLATIONS The truncated octahedron exists in three different Convex Uniform Honeycomb s ( Space-filling Tessellations ): The Cell-transitive Bitruncated Cubic Honeycomb can also be seen as the Voronoi Tessellation of the Body-centred Cubic Lattice . REFERENCES
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