Truncated octahedron

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In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six equilateral square pyramids, one at each of the octahedron's vertices. It is also the cantitruncated form of a regular tetrahedron. The truncated octahedron has 14 faces (8 regular hexagons and 6 squares), 36 edges, and 24 vertices. Since each of its faces has point symmetry, the truncated octahedron is a 6-zonohedron. It is also the Goldberg polyhedron GIV(1,1), containing square and hexagonal faces. Like the cube, it can tessellate (or "pack") 3-dimensional space, as a permutohedron. The truncated octahedron is also known as the orthic tetrakaidecahedron. Buckminster Fuller called it the "mecon". Its dual polyhedron is the tetrakis hexahedron. If the original truncated octahedron has unit edge length, then its dual tetrakis hexahedron has edge lengths ⁠9/8⁠√2 and ⁠3/2⁠√2.

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