Dodecagonal-truncated tetrahedral duoprism
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Dodecagonal-truncated tetrahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Twatut |
Coxeter diagram | x12o x3x3o () |
Elements | |
Tera | 4 triangular-dodecagonal duoprisms, 12 truncated tetrahedral prisms, 4 hexagonal-dodecagonal duoprisms |
Cells | 48 triangular prisms, 48 hexagonal prisms, 12 truncated tetrahedra, 6+12 dodecagonal prisms |
Faces | 48 triangles, 72+144 squares, 48 hexagons, 12 dodecagons |
Edges | 72+144+144 |
Vertices | 144 |
Vertex figure | Digonal disphenoidal pyramid, edge lengths 1, √3, √3 (base triangle), √2+√3 (top), √2 (side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tuttip–tut–tuttip: 150° |
Titwadip-twip-hitwadip: | |
Titwadip–trip–tuttip: 90° | |
Hitwadip-hip-tuttip: 90° | |
Hitwadip–twip–hitwadip: | |
Central density | 1 |
Number of external pieces | 20 |
Level of complexity | 30 |
Related polytopes | |
Army | Twatut |
Regiment | Twatut |
Dual | Dodecagonal-triakis tetrahedral duotegum |
Conjugate | Dodecagrammic-truncated tetrahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A3×I2(12), order 576 |
Convex | Yes |
Nature | Tame |
The dodecagonal-truncated tetrahedral duoprism or twatut is a convex uniform duoprism that consists of 12 truncated tetrahedral prisms, 4 hexagonal-dodecagonal duoprisms, and 4 triangular-dodecagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-dodecagonal duoprism, and 2 hexagonal-dodecagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of a dodecagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:
Representations[edit | edit source]
A dodecagonal-truncated tetrahedral duoprism has the following Coxeter diagrams:
- x12o x3x3o (full symmetry)
- x6x x3x3o () (A3×G2 symmetry, dodecagons as dihexagons)
External links[edit | edit source]
Klitzing, Richard. "n-tut-dip".