Decagonal-truncated dodecahedral duoprism |
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Rank | 5 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Datid |
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Coxeter diagram | x10o x5x3o () |
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Elements |
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Tera | 20 triangular-decagonal duoprisms, 12 decagonal duoprisms |
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Cells | 200 triangular prisms, 30+60+120 decagonal prisms, 10 truncated dodecahedra |
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Faces | 200 triangles, 300+600 squares, 60+120 decagons |
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Edges | 300+600+600 |
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Vertices | 600 |
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Vertex figure | Digonal disphenoidal pyramid, edge lengths 1, √(5+√5)/2, √(5+√5)/2 (base triangle), √(5+√5)/2 (top), √2 (side edges) |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Diteral angles | Tiddip–tid–tiddip: 144° |
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| Tradedip–dip–dedip: |
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| Dedip–dip–dedip: |
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| Tradedip–trip–tiddip: 90° |
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| Dedip–dip–tiddip: 90° |
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Central density | 1 |
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Number of external pieces | 42 |
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Level of complexity | 30 |
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Related polytopes |
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Army | Datid |
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Regiment | Datid |
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Dual | Decagonal-triakis icosahedral duotegum |
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Conjugate | Decagrammic-quasitruncated great stellated dodecahedral duoprism |
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Abstract & topological properties |
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Euler characteristic | 2 |
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Orientable | Yes |
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Properties |
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Symmetry | H3×I2(10), order 2400 |
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Convex | Yes |
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Nature | Tame |
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The decagonal-truncated dodecahedral duoprism or datid is a convex uniform duoprism that consists of 10 truncated dodecahedral prisms, 12 decagonal duoprisms, and 20 triangular-decagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-decagonal duoprism, and 2 decagonal duoprisms.
The vertices of a decagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
A decagonal-truncated dodecahedral duoprism has the following Coxeter diagrams:
- x10o x5x3o (full symmetry)
- x5x x5x3o (decagons as dipentagons)