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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 ...
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.
The middle image is the uniform truncated cube; it is represented by a Schläfli symbol t{p,q,...}. A bitruncation is a deeper truncation, removing all the original edges, but leaving an interior part of the original faces. Example: a truncated octahedron is a bitruncated cube: t{3,4} = 2t{4,3}.
An example is the rhombicuboctahedron, constructed by separating the cube or octahedron's faces from the centroid and filling them with squares. [8] Snub is a construction process of polyhedra by separating the polyhedron faces, twisting their faces in certain angles, and filling them up with equilateral triangles .
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.
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 .
In geometry, the rectified truncated octahedron is a convex polyhedron, constructed as a rectified, truncated octahedron. It has 38 faces: 24 isosceles triangles, ...
Octahedron-first parallel projection into 3 dimensions, with octahedral cells highlighted. The octahedron-first parallel projection of the truncated 16-cell into 3-dimensional space has the following structure: The projection envelope is a truncated octahedron. The 6 square faces of the envelope are the images of 6 of the octahedral cells.