Great heptagrammic antiprismatic prism
Great heptagrammic antiprismatic prism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Gishappip |
Coxeter diagram | x2s2s14/3o () |
Elements | |
Cells | 14 triangular prisms, 2 great heptagrammic prisms, 2 great heptagrammic antiprisms |
Faces | 28 triangles, 14+14 squares, 4 great heptagrams |
Edges | 14+28+28 |
Vertices | 28 |
Vertex figure | Isosceles trapezoidal pyramid, edge lengths 1, 1, 1, 2cos(3π/7) (base), √2 (legs) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Trip–4–giship: |
Gishap–7/3–giship: 90° | |
Gishap–3–trip: 90° | |
Trip–4–trip: | |
Heights | Gishap atop gishap: 1 |
Giship atop gyro giship: | |
Number of external pieces | 74 |
Related polytopes | |
Army | Semi-uniform heappip |
Regiment | Gishappip |
Dual | Great heptagrammic antitegmatic tegum |
Conjugate | Heptagonal antiprismatic prism |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(14)×A1)+×A1, order 56 |
Convex | No |
Nature | Tame |
The great heptagrammic antiprismatic prism or gishappip is a prismatic uniform polychoron that consists of 2 great heptagrammic antiprisms, 2 great heptagrammic prisms, and 14 triangular prisms. Each vertex joins 1 great heptagrammic antiprism, 1 great heptagrammic prism, and 3 triangular prisms. As the name suggests, it is a prism based on the great heptagrammic antiprism. Being a prism based on an orbiform polytope, it is also a segmentochoron.
Vertex coordinates[edit | edit source]
The vertices of a great heptagrammic antiprismatic prism, centered at the origin and with edge length 2sin(3π/7), are given by the following points, as well as the central inversions of their first three coordinates:
where
Representations[edit | edit source]
A great heptagrammic antiprismatic prism has the following Coxeter diagrams:
- x2s2s14/3o (full symmetry)
- x2s2s7/3s ()
- xx xo7/3ox&#x (great heptagrammic prism atop gyrated great heptagrammic prism)
External links[edit | edit source]
- Bowers, Jonathan. "Category B: Antiduoprisms".
- Wikipedia contributors. "Uniform antiprismatic prism".