Truncated octahedron | |
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(Click here for rotating model) | |
Type | Archimedean solid Uniform polyhedron |
Elements | F = 14, E = 36, V = 24 (χ = 2) |
Faces by sides | 6{4}+8{6} |
Conway notation | tO bT |
Schläfli symbols | t{3,4} tr{3,3} or |
t0,1{3,4} or t0,1,2{3,3} | |
Wythoff symbol | 2 4 | 3 3 3 2 | |
Coxeter diagram | |
Symmetry group | Oh, B3, [4,3], (*432), order 48 Th, [3,3] and (*332), order 24 |
Rotation group | O, [4,3]+, (432), order 24 |
Dihedral angle | |
References | U08, C20, W7 |
Properties | Semiregular convex parallelohedron permutohedron zonohedron |
Colored faces |
4.6.6 (Vertex figure) |
Tetrakis hexahedron (dual polyhedron) |
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 9/8√2 and 3/2√2.
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