Square-truncated dodecahedral duoprism
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Square-truncated dodecahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Squatid |
Coxeter diagram | x4o x5x3o () |
Elements | |
Tera | 4 truncated dodecahedral prisms, 12 square-decagonal duoprisms, 20 triangular-square duoprisms |
Cells | 4 truncated dodecahedra, 48 decagonal prisms, 30+60 cubes, 80 triangular prisms |
Faces | 48 decagons, 60+120+240 squares, 80 triangles |
Edges | 120+240+240 |
Vertices | 240 |
Vertex figure | Isosceles triangular scalene, edge lengths 1, √(5+√5)/2, √(5+√5)/2 (base triangle), √2 (top and side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tiddip–tid–tiddip: 90° |
Tisdip–trip–tiddip: 90° | |
Squadedip–dip–tiddip: 90° | |
Tisdip–cube–squadedip: | |
Squadedip–cube–squadedip: | |
Height | Tiddip atop tiddip: 1 |
Central density | 1 |
Related polytopes | |
Army | Squatid |
Regiment | Squatid |
Dual | Square-triakis icosahedral duotegum |
Conjugate | Square-quasitruncated great stellated dodecahedral duoprism |
Abstract & topological properties | |
Flag count | 28800 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | H3×B2, order 960 |
Convex | Yes |
Nature | Tame |
The square-truncated dodecahedral duoprism or squatid is a convex uniform duoprism that consists of 4 truncated dodecahedral prisms, 12 square-decagonal duoprisms and 20 triangular-square duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-square duoprism, and 2 square-decagonal duoprisms. It is a duoprism based on a square and a truncated dodecahedron, which makes it a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a square-truncated dodecahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
Representations[edit | edit source]
A square-truncated dodecahedral duoprism has the following Coxeter diagrams:
- x4o x5x3o (full symmetry)
- x x x5x3o (truncated dodecahedral prismatic prism)
External links[edit | edit source]
- Klitzing, Richard. "squatid".