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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 G IV (1,1), containing square and hexagonal faces. Like the cube, it can tessellate (or "pack") 3-dimensional space, as a ...
Truncated quasi-regular (scalene triangular vertex figures), p.q.r Wythoff symbol p q r| Snub quasi-regular (pentagonal, hexagonal, or octagonal vertex figures), Wythoff symbol p q r| Prisms (truncated hosohedra), Antiprisms and crossed antiprisms (snub dihedra) The format of each figure follows the same basic pattern image of polyhedron
They are obtained by snubification of the truncated octahedron, truncated cuboctahedron and the truncated icosidodecahedron - the three convex truncated quasiregular polyhedra. The only snub polyhedron with the chiral octahedral group of symmetries is the snub cube. Only the icosahedron and the great icosahedron are also regular polyhedra.
The truncated order-4 octahedral honeycomb, t 0,1 {3,4,4}, has truncated octahedron and square tiling facets, with a square pyramid vertex figure. Bitruncated order-4 octahedral honeycomb [ edit ]
In three-dimensional hyperbolic geometry, the alternated hexagonal tiling honeycomb, h{6,3,3}, or , is a semiregular tessellation with tetrahedron and triangular tiling cells arranged in an octahedron vertex figure. It is named after its construction, as an alteration of a hexagonal tiling honeycomb.
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular ), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and δ S +1 , where δ S is the silver ratio, √ 2 +1.
A bitruncated cube is a truncated octahedron. A bitruncated cubic honeycomb - Cubic cells become orange truncated octahedra, and vertices are replaced by blue truncated octahedra. In geometry, a bitruncation is an operation on regular polytopes. The original edges are lost completely and the original faces remain as smaller copies of themselves.
The bitruncated cubic honeycomb, a convex honeycomb whose truncated octahedron cells are deformed slightly to form the Kelvin structure. In two dimensions, the subdivision of the plane into cells of equal area with minimum average perimeter is given by the hexagonal tiling, but although the first record of this honeycomb conjecture goes back to the ancient Roman scholar Marcus Terentius Varro ...