Square-heptagrammic duoprism
(Redirected from 7/2-4 duoprism)
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| Square-heptagrammic duoprism | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Space | Spherical |
| Bowers style acronym | Sashedip |
| Info | |
| Coxeter diagram | x4o x7/2o |
| Symmetry | BC2×I2(7), order 112 |
| Army | Semi-uniform squahedip |
| Regiment | Sashedip |
| Elements | |
| Vertex figure | Digonal disphenoid, 2cos(2π/7) (base 1) and √2 (base 2 and sides) |
| Cells | 7 cubes, 4 heptagrammic prisms |
| Faces | 7+28 squares, 4 heptagrams |
| Edges | 28+28 |
| Vertices | 28 |
| Measures (edge length 1) | |
| Circumradius | √2+csc2(2π/7)/2 ≈ 0.95341 |
| Hypervolume | 7/[4tan(2π/7)] ≈ 1.39558 |
| Dichoral angles | Cube–4–cube: 3π/7 ≈ 77.14286° |
| Ship–7/2–ship: 90° | |
| Cube–4–ship: 90° | |
| Central density | 2 |
| Related polytopes | |
| Dual | Square-heptagrammic duotegum |
| Conjugates | Square-heptagonal duoprism, Square-great heptagrammic duoprism |
| Properties | |
| Convex | No |
| Orientable | Yes |
| Nature | Tame |
The square-heptagrammic duoprism, also known as sashedip or the 4-7/2 duoprism, is a uniform duoprism that consists of 7 cubes and 4 heptagrammic prisms, with 2 of each meeting at each vertex.
The name can also refer to the square-great heptagrammic duoprism.
Vertex coordinates[edit | edit source]
The coordinates of a square-heptagrammic duoprism, centered at the origin and with edge length 2sin(2π/7), are given by:
- (±sin(2π/7), ±sin(2π/7), 1, 0),
- (±sin(2π/7), ±sin(2π/7), cos(2π/7), ±sin(2π/7)),
- (±sin(2π/7), ±sin(2π/7), cos(4π/7), ±sin(4π/7)),
- (±sin(2π/7), ±sin(2π/7), cos(6π/7), ±sin(6π/7)).
External links[edit | edit source]
Bowers, Jonathan. "Category A: Duoprisms".
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