Heptagrammic-dodecagonal duoprism
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Heptagrammic-dodecagonal duoprism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Coxeter diagram | x7/2o x12o () |
Elements | |
Cells | 12 heptagrammic prisms, 7 dodecagonal prisms |
Faces | 84 squares, 12 heptagrams, 7 dodecagons |
Edges | 84+84 |
Vertices | 84 |
Vertex figure | Digonal disphenoid, edge lengths 2cos(2π/7) (base 1), (√6+√2)/2 (base 2), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Ship–7/2–ship: 150° |
Ship–4–twip: 90° | |
Twip–12–twip: | |
Central density | 2 |
Number of external pieces | 26 |
Level of complexity | 12 |
Related polytopes | |
Army | Semi-uniform hetwadip |
Dual | Heptagrammic-dodecagonal duotegum |
Conjugates | Heptagonal-dodecagonal duoprism, Heptagonal-dodecagrammic duoprism, Heptagrammic-dodecagrammic duoprism, Great heptagrammic-dodecagonal duoprism, Great heptagrammic-dodecagrammic duoprism |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | I2(7)×I2(12), order 336 |
Convex | No |
Nature | Tame |
The heptagrammic-dodecagonal duoprism, also known as the 7/2-12 duoprism, is a uniform duoprism that consists of 12 heptagrammic prisms and 7 dodecagonal prisms, with 2 of each at each vertex.
The name can also refer to the great heptagrammic-dodecagonal duoprism.
Vertex coordinates[edit | edit source]
The coordinates of a heptagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(2π/7), are given by:
where j = 2, 4, 6.
Representations[edit | edit source]
A heptagrammic-dodecagonal duoprism has the following Coxeter diagrams:
- x7/2o x12o (full symmetry)
- x6x x7/2o () (G2×I2(7) symmetry, dodecagons as dihexagons)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "nd-mb-dip".