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 (or 180° rotational symmetry), the truncated octahedron is a zonohedron. __TOC__

Cartesian coordinates

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All permutations 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.

Geometric relations

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Truncated octahedra are able to tessellate 3-dimensional space, forming an Andreini tessellation. This tessellation can also be seen as the Voronoi tessellation of the body-centred cubic lattice.

Related polyhedra

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Compare:

truncatedhexahedron.jpg]]cuboctahedron.jpg]]

External links

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• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra
• ^* Uniform space-filling using only truncated octahedra

Uniform polyhedra | Archimedean solids | Zonohedra

Afgeknotte octaëder | 切頂八面体 | Ośmiościan ścięty | Octaedro truncado