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Compound Of Four Octahedra
The compound of four octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then rotating each by 60 degrees about a separate axis (that passes through the centres of two opposite octahedral faces). Its dual is the compound of four cubes. Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the permutations of : (±2, ±1, ±2) See also * Compound of three octahedra * Compound of five octahedra * Compound of ten octahedra * Compound of twenty octahedra *Compound of four cubes The compound of four cubes or Bakos compound is a face-transitive polyhedron compound of four cubes with octahedral symmetry. It is the dual of the compound of four octahedra. Its surface area is 687/77 square lengths of the edge. Its Cartesian c ... References *. Polyhedral compounds {{polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
UC12-4 Octahedra
UC1 may refer to: * ** , a German World War I submarine * German Type UC I submarine The Type UC I coastal submarines were a class of small minelaying U-boats built in Germany during the early part of World War I. They were the first operational minelaying submarines in the world (although the Russian submarine ''Krab'' was laid ... of World War II * , a Danish private electric sub See also * UC (other) {{Letter-NumberCombDisambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Polyhedron Compound
In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e. the symmetry group of the compound acts transitively on the compound's vertices. The uniform polyhedron compounds were first enumerated by John Skilling in 1976, with a proof that the enumeration is complete. The following table lists them according to his numbering. The prismatic compounds of prisms ( UC20 and UC21) exist only when , and when and are coprime. The prismatic compounds of antiprisms ( UC22, UC23, UC24 and UC25) exist only when , and when and are coprime. Furthermore, when , the antiprisms degenerate into tetrahedra with digon In geometry, a digon is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Twenty Octahedra
The compound of twenty octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 20 octahedra (considered as triangular antiprisms). It is a special case of the compound of 20 octahedra with rotational freedom, in which pairs of octahedral vertices coincide. Related polyhedra This compound shares its edge arrangement with the great dirhombicosidodecahedron, the great disnub dirhombidodecahedron, and the compound of twenty tetrahemihexahedra. It may be constructed as the exclusive or of the two enantiomorphs of the great snub dodecicosidodecahedron. See also *Compound of three octahedra *Compound of four octahedra *Compound of five octahedra The compound of five octahedra is one of the five regular polyhedron compounds. This polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund Hess in 1876. It is unique among the regular ... * Compound of ten octahedra References *. Polyhe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Of Ten Octahedra
The compounds of ten octahedra UC15 and UC16 are two uniform polyhedron compounds. They are composed of a symmetric arrangement of 10 octahedron, octahedra, considered as triangular antiprisms, aligned with the axes of three-fold rotational symmetry of an icosahedron. The two compounds differ in the orientation of their octahedra: each compound may be transformed into the other by rotating each octahedron by 60 degrees. Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the cyclic permutations of : (0, ±(τ−1 + 2''s''τ), ±(τ − 2sτ−1)) : (±( − ''s''τ2), ±( + ''s''(2τ − 1)), ±( + ''s''τ−2)) : (±(τ−1 − ''s''τ), ±(τ + ''s''τ−1), ±3''s'') where τ = (1 + )/2 is the golden ratio (sometimes written φ) and ''s'' is either +1 or −1. Setting ''s'' = −1 gives UC15, while ''s'' = +1 gives UC16. See also *Compound of three octahedra *Compound of four octahedra *Compound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |