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ditrigonary polyhedra
In geometry, a ditrigonary polyhedron is a uniform star polyhedron with Wythoff symbol: 3 | p q. There are three of them, each including two types of faces, being of triangles, pentagons, or pentagrams. Their vertex figures have the same vertex arrangement, but different edges.
They have 20 vertices, shared with the regular dodecahedron. They are also related to the compound of five cubes which shares the same vertex arrangement and the same edge arrangement.
||32
20 , 12 ||24
12 , 12 ||32
20 , 12
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!Image
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!Vertex figure
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!Wythoff symbol
!3 | 2 5
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!3 | 5/2 3
!3 | 5/3 5
!3 | 3/2 5
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!Coxeter diagram
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|File:Small ditrigonal icosidodecahedron cd.png
|File:Ditrigonal dodecadodecahedron cd.png
|File:Great ditrigonal icosidodecahedron cd.png
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== Related polytopes ==
Norman Johnson discovered three related antiprism-like star polytopes, published in 1966 in his Ph.D. Dissertation, now named the Johnson antiprisms. These have these ditrigonary star polyhedra as their bases.〔Johnson, 1966〕 They all have 40 vertices, 40 total cells, and 180 total faces. They have 184 (small ditrigonary icosidodecahedral antiprism), 168 (ditrigonary dodecadodecahedral antiprism), and 184 (great ditrigonary icosidodecahedral antiprism) edges respectively. Stella4D software can render these as models 966, 967, and 968. Their Coxeter-Dynkin diagrams are File:Small ditrigonal icosidodecahedron cd.png , File:Ditrigonal dodecadodecahedron cd.png , and File:Great ditrigonal icosidodecahedron cd.png respectively.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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