Hexagonal-tetrahedral duoprism
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Hexagonal-tetrahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Hatet |
Coxeter diagram | x6o x3o3o () |
Elements | |
Tera | 6 tetrahedral prisms, 4 triangular-hexagonal duoprisms |
Cells | 6 tetrahedra, 24 triangular prisms, 6 hexagonal prisms |
Faces | 24 triangles, 36 squares, 4 hexagons |
Edges | 24+36 |
Vertices | 24 |
Vertex figure | Triangular scalene, edge lengths 1 (base triangle), √3 (top), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tepe–tet–tepe: 120° |
Tepe–trip–thiddip: 90° | |
Thiddip–hip–thiddip: | |
Heights | Hig atop thiddip: |
Hip atop perp hip: | |
Central density | 1 |
Number of external pieces | 10 |
Level of complexity | 10 |
Related polytopes | |
Army | Hatet |
Regiment | Hatet |
Dual | Hexagonal-tetrahedral duotegum |
Conjugate | None |
Abstract & topological properties | |
Flag count | 2880 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A3×G2, order 288 |
Convex | Yes |
Nature | Tame |
The hexagonal-tetrahedral duoprism or hatet is a convex uniform duoprism that consists of 6 tetrahedral prisms and 4 triangular-hexagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-hexagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of a hexagonal-tetrahedral duoprism of edge length 1 are given by all even sign changes of the last three coordinates of:
Representations[edit | edit source]
A hexagonal-tetrahedral duoprism has the following Coxeter diagrams:
- x6o x3o3o (full symmetry)
- x3x x3o3o (hexagons as ditrigons)
- ox3oo xx6oo&#x (hexagon atop triangular-hexagonal duoprism)
- ox3oo xx3xx&#x
- ox xo xx6oo&#x (hexagonal prism atop orthogonal hexagonal prism)
- ox xo xx3xx&#x
- oox xxx3xxx&#x
- xxxx3xxxx&#x
External links[edit | edit source]
- Klitzing, Richard. "hatet".