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Truncated octahedron

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Type Archimedean
Faces6 squares
8 hexagons
Edges36
Vertices24
Vertex configuration4,6,6
Symmetry groupoctahedral (Oh)
Dual polyhedron tetrakis hexahedron
Propertiesconvex, semi-regular (vertex-uniform), zonohedron

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.


Canonical coordinates for the vertices of a truncated octahedron centered at the origin are (±2, ±1, 0), (0, ±2, ±1), (±1, 0, ±2), (±1, ±2, 0), (0, ±1, ±2), (±2, 0, ±1), note that the coordinates form a lot of rectangles parallel with the coordinate system axes.


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.

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Archimedean solids

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