Search results
Results from the WOW.Com Content Network
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.
Example: a truncated octahedron is a bitruncated cube: t{3,4} = 2t{4,3}. A complete bitruncation, called a birectification, reduces original faces to points. For polyhedra, this becomes the dual polyhedron. Example: an octahedron is a birectification of a cube: {3,4} = 2r{4,3}.
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 truncated order-4 hexagonal tiling honeycomb, t 0,1 {6,3,4}, has octahedron and truncated hexagonal tiling facets, with a square pyramid vertex figure. It is similar to the 2D hyperbolic truncated order-4 apeirogonal tiling , t{∞,4}, with apeirogonal and square faces:
Simple examples of Goldberg polyhedra include the dodecahedron and truncated icosahedron. Other forms can be described by taking a chess knight move from one pentagon to the next: first take m steps in one direction, then turn 60° to the left and take n steps.
The coordinates of the vertices for one octahedron represent a hyperplane of integers in 4-space, specifically permutations of (1,2,3,4). The tessellation is formed by translated copies within the hyperplane. The tessellation is the highest tessellation of parallelohedrons in 3-space.
(In the example image the vertices (3, 2, 1, 4) and (2, 3, 1, 4) are connected by a blue edge and differ by swapping 2 and 3 on the first two places. The values 2 and 3 differ by 1. All blue edges correspond to swaps of coordinates on the first two places.) The number of facets is 2 n − 2, because they correspond to non-empty proper subsets S ...
In geometry, a tetrakis hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube [2]) is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid. It can be called a disdyakis hexahedron or hexakis tetrahedron as the dual of an omnitruncated tetrahedron, and as the barycentric subdivision of a ...