Heptagrammic antiprismatic prism
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Heptagrammic antiprismatic prism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Shappip |
Coxeter diagram | x2s2s14/2o () |
Elements | |
Cells | 14 triangular prisms, 2 heptagrammic prisms, 2 heptagrammic antiprisms |
Faces | 28 triangles, 14+14 squares, 4 heptagrams |
Edges | 14+28+28 |
Vertices | 28 |
Vertex figure | Isosceles trapezoidal pyramid, edge lengths 1, 1, 1, 2cos(2π/7) (base), √2 (legs) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Trip–4–trip: |
Trip–4–ship: | |
Shap–7/2–ship: 90° | |
Shap–3–trip: 90° | |
Heights | Shap atop shap: 1 |
Ship atop ship: | |
Number of external pieces | 46 |
Related polytopes | |
Army | Semi-uniform squahedip |
Regiment | Shappip |
Dual | Heptagrammic antitegmatic tegum |
Conjugate | Great heptagrammic retroprismatic prism |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | I2(7)×A1×A1, order 56 |
Convex | No |
Nature | Tame |
The heptagrammic antiprismatic prism or shappip is a prismatic uniform polychoron that consists of 2 heptagrammic antiprisms, 2 heptagrammic prisms, and 14 triangular prisms. Each vertex joins 1 heptagrammic antiprism, 1 heptagrammic prism, and 3 triangular prisms. As the name suggests, it is a prism based on the heptagrammic antiprism. Being a prism based on an orbiform polytope, it is also a segmentochoron.
Vertex coordinates[edit | edit source]
The vertices of a heptagrammic antiprismatic prism, centered at the origin and with edge length 2sin(2π/7), are given by:
where
Representations[edit | edit source]
A heptagrammic antiprismatic prism has the following Coxeter diagrams:
- x2s2s14/2o (full symmetry)
- x2s2s7/2s
- xx xo7/2ox&#x (heptagrammic prism atop heptagrammic prism)
External links[edit | edit source]
- Bowers, Jonathan. "Category B: Antiduoprisms".
- Wikipedia contributors. "Uniform antiprismatic prism".