Heptagonal-decagrammic duoprism
(Redirected from 7-10/3 duoprism)
Heptagonal-decagrammic duoprism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Hestadedip |
Coxeter diagram | x7o x10/3o () |
Elements | |
Cells | 10 heptagonal prisms, 7 decagrammic prisms |
Faces | 70 squares, 10 heptagons, 7 decagrams |
Edges | 70+70 |
Vertices | 70 |
Vertex figure | Digonal disphenoid, edge lengths 2cos(π/7) (base 1), √(5–√5)/2 (base 2), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Stiddip–10/3–stiddip: |
Hep–4–stiddip: 90° | |
Hep–7–hep: 72° | |
Central density | 3 |
Number of external pieces | 27 |
Level of complexity | 12 |
Related polytopes | |
Army | Semi-uniform hedadip |
Regiment | Hestadedip |
Dual | Heptagonal-decagrammic duotegum |
Conjugates | Heptagonal-decagonal duoprism, Heptagrammic-decagonal duoprism, Heptagrammic-decagrammic duoprism, Great heptagrammic-decagonal duoprism, Great heptagrammic-decagrammic duoprism |
Abstract & topological properties | |
Flag count | 1680 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | I2(7)×I2(10), order 280 |
Convex | No |
Nature | Tame |
The heptagonal-decagrammic duoprism, also known as hestadedip or the 7-10/3 duoprism, is a uniform duoprism that consists of 10 heptagonal prisms and 7 decagrammic prisms, with 2 of each at each vertex.
Vertex coordinates[edit | edit source]
The coordinates of a heptagonal-decagrammic duoprism, centered at the origin and with edge length 2sin(π/7), are given by:
- ,
- ,
- ,
- ,
- ,
- ,
where j = 2, 4, 6.
Representations[edit | edit source]
A heptagonal-decagrammic duoprism duoprism has the following Coxeter diagrams:
- x7o x10/3o () (full symmetry)
- x5/3x x7o () (H2×I2(7) symmetry, decagons as dipentagons)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "nd-mb-dip".