Truncated octahedron

Truncated octahedron
TypeArchimedean solid,
Parallelohedron,
Permutohedron,
Plesiohedron,
Zonohedron
Faces14
Edges36
Vertices24
Symmetry groupoctahedral symmetry
Dual polyhedrontetrakis hexahedron
Vertex figure
Net

In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. 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 was called the "mecon" by Buckminster Fuller.[1]

Its dual polyhedron is the tetrakis hexahedron. If the original truncated octahedron has unit edge length, its dual tetrakis hexahedron has edge lengths 9/82 and 3/22.

  1. ^ "Truncated Octahedron". Wolfram Mathworld.