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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 ...
The cyclotruncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated cube and octahedron cells, in a square antiprism vertex figure. It has a Coxeter diagram . Perspective view from center of octahedron. It can be seen as somewhat analogous to the trioctagonal tiling, which has truncated square and triangle ...
The bitruncated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of truncated octahedra (or, equivalently, bitruncated cubes). It has 4 truncated octahedra around each vertex. Being composed entirely of truncated octahedra, it is cell-transitive.
The cantic cubic honeycomb, cantic cubic cellulation or truncated half cubic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of truncated octahedra, cuboctahedra and truncated tetrahedra in a ratio of 1:1:2. Its vertex figure is a rectangular pyramid.
English: A diagram showing how an en:octahedron is made into a truncated octahedron (blue) by removing square pyramids from each face (red). Français : Diagramme montrant comment on obtient un tétrakaidécaèdre d'Archimède (ou octaèdre tronqué ) en tronquant les 6 sommets d'un octaèdre régulier à hauteur du tiers de chaque arête.
For example, tC represents a truncated cube, and taC, parsed as t(aC), is (topologically) a truncated cuboctahedron. The simplest operator dual swaps vertex and face elements; e.g., a dual cube is an octahedron: dC = O. Applied in a series, these operators allow many higher order polyhedra to be generated.
Two of the truncated octahedra project onto a truncated octahedron lying in the center of the envelope. Six cuboidal volumes join the square faces of this central truncated octahedron to the center of the octagonal faces of the great rhombicuboctahedron. These are the images of 12 of the cubical cells, a pair of cells to each image.
Regular polyhedra with even-order vertices can also be snubbed as alternated truncations, like the snub octahedron, as {,}, , is the alternation of the truncated octahedron, {,}, and . The snub octahedron represents the pseudoicosahedron , a regular icosahedron with pyritohedral symmetry .