Triangular-heptagonal duoprismatic prism
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Triangular-heptagonal duoprismatic prism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Trahep |
Coxeter diagram | x x3o x7o () |
Elements | |
Tera | 7 triangular-square duoprisms, 2 triangular-heptagonal duoprisms, 3 square-heptagonal duoprisms |
Cells | 7+14 triangular prisms, 21 cubes, 3+6 heptagonal prisms |
Faces | 14 triangles, 21+21+42 squares, 6 heptagons |
Edges | 21+42+42 |
Vertices | 42 |
Vertex figure | Digonal disphenoidal pyramid, edge lengths 1 (disphenoid base 1), 2cos(π/7) (disphenoid base 2), √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tisdip–trip–tisdip: |
Theddip–trip–tisdip: 90° | |
Squahedip–cube–tisdip: 90° | |
Theddip–hep–squahedip: 90° | |
Squahedip–hep–squahedip: 60° | |
Heights | Theddip atop theddip: 1 |
Hep atop squahedip: | |
Central density | 1 |
Number of external pieces | 12 |
Level of complexity | 30 |
Related polytopes | |
Army | Trahep |
Regiment | Trahep |
Dual | Triangular-heptagonal duotegmatic tegum |
Conjugates | Triangular-heptagrammic duoprismatic prism, Triangular-great heptagrammic duoprismatic prism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A2×I2(7)×A1, order 168 |
Convex | Yes |
Nature | Tame |
The triangular-heptagonal duoprismatic prism or trahep, also known as the triangular-heptagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-heptagonal duoprisms, 3 square-heptagonal duoprisms, and 7 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-heptagonal duoprisms, and 1 triangular-heptagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a triangular-heptagonal duoprismatic prism of edge length 2sin(π/7) are given by:
where j = 2, 4, 6.
Representations[edit | edit source]
A triangular-heptagonal duoprismatic prism has the following Coxeter diagrams:
- x x3o x7o (full symmetry)
- xx3oo xx7oo&#x (triangular-heptagonal duoprism atop triangular-heptagonal duoprism)
- ox xx xx7oo&#x (heptagonal prism atop square-heptagonal duoprism)