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3D model of a truncated cube. 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.
Types of truncation on a square, {4}, showing red original edges, and new truncated edges in cyan. A uniform truncated square is a regular octagon, t{4}={8}. A complete truncated square becomes a new square, with a diagonal orientation. Vertices are sequenced around counterclockwise, 1-4, with truncated pairs of vertices as a and b.
The runcicantic order-5 cubic honeycomb is a uniform compact space-filling tessellation (or honeycomb), with Schläfli symbol h 2,3 {4,3,5}. It has truncated dodecahedron, truncated icosidodecahedron, and truncated tetrahedron cells, with an irregular tetrahedron vertex figure.
Two chiral copies of the snub cube, as alternated (red or green) vertices of the truncated cuboctahedron. A snub cube can be constructed from a rhombicuboctahedron by rotating the 6 blue square faces until the 12 white square faces become pairs of equilateral triangle faces. In geometry, a snub is an operation applied to a polyhedron.
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.
In geometry, a triakis octahedron (or trigonal trisoctahedron [1] or kisoctahedron [2]) is an Archimedean dual solid, or a Catalan solid.Its dual is the truncated cube.. It can be seen as an octahedron with triangular pyramids added to each face; that is, it is the Kleetope of the octahedron.
Vertices are truncated, forming new red rectified cube cells. In geometry , a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices , creating a new facet in place of each edge and of each vertex.
In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube. There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square faces of the 8-cube.