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Pentagonal Icositetrahedron
In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron is a Catalan solid which is the dual of the snub cube. In crystallography it is also called a gyroid. It has two distinct forms, which are mirror images (or " enantiomorphs") of each other. Construction The pentagonal icositetrahedron can be constructed from a snub cube without taking the dual. Square pyramids are added to the six square faces of the snub cube, and triangular pyramids are added to the eight triangular faces that do not share an edge with a square. The pyramid heights are adjusted to make them coplanar with the other 24 triangular faces of the snub cube. The result is the pentagonal icositetrahedron. Cartesian coordinates Denote the tribonacci constant by t\approx 1.839\,286\,755\,21. (See snub cube for a geometric explanation of the tribonacci constant.) Then Cartesian coordinates for the 38 vertices of a pentagonal icositetrahedron centered at the origin, are as follows: *the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagonal Icositetrahedron
In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron is a Catalan solid which is the dual of the snub cube. In crystallography it is also called a gyroid. It has two distinct forms, which are mirror images (or " enantiomorphs") of each other. Construction The pentagonal icositetrahedron can be constructed from a snub cube without taking the dual. Square pyramids are added to the six square faces of the snub cube, and triangular pyramids are added to the eight triangular faces that do not share an edge with a square. The pyramid heights are adjusted to make them coplanar with the other 24 triangular faces of the snub cube. The result is the pentagonal icositetrahedron. Cartesian coordinates Denote the tribonacci constant by t\approx 1.839\,286\,755\,21. (See snub cube for a geometric explanation of the tribonacci constant.) Then Cartesian coordinates for the 38 vertices of a pentagonal icositetrahedron centered at the origin, are as follows: *the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
