Square cupolic prism
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Square cupolic prism | |
---|---|
Rank | 4 |
Type | Segmentotope |
Notation | |
Bowers style acronym | Squacupe |
Coxeter diagram | xx ox4xx&#x |
Elements | |
Cells | 4 triangular prisms, 1+4 cubes, 2 square cupolas, 1 octagonal prism |
Faces | 8 triangles, 2+4+4+4+8+8 squares, 2 octagons |
Edges | 4+8+8+8+8+16 |
Vertices | 8+16 |
Vertex figures | 8 isosceles trapezoidal pyramids, base edge lengths 1, √2, √2, √2, side edge length √2 |
16 irregular tetrahedra, edge lengths 1 (1), √2 (4), and √2+√2 (1) | |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | trip–4–cube: |
Cube–4–cube: 135º | |
Squacu–4–trip: 90° | |
Squacu–4–cube: 90° | |
Squacu–8–op: 90° | |
Trip–4–op: | |
Cube–4–op: 45° | |
Heights | Squacu atop squacu: 1 |
Cube atop op: | |
Central density | 1 |
Related polytopes | |
Army | Squacupe |
Regiment | Squacupe |
Dual | Semibisected tetragonal trapezohedral tegum |
Conjugate | Retrograde square cupolic prism |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B2×A1×I, order 16 |
Convex | Yes |
Nature | Tame |
The square cupolic prism, or squacupe, is a CRF segmentochoron (designated K-4.69 on Richard Klitzing's list). It consiss of 2 square cupolas, 4 triangular prisms, 1+4 cubes, and 1 octagonal prism.
As the name suggests, it is a prism based on the square cupola. As such, it is a segmentochoron between two square cupolas. It can also be viewed as a segmentochoron between an octagonal prism and a cube.
Two square cupolic prisms can be attached to opposite octagonal prismatic cells of the square-octagonal duoprism to produce a small rhombicuboctahedral prism.
Vertex coordinates[edit | edit source]
Coordinates of the vertices of a square cupolic prism of edge length 1 centered at the origin are given by:
External links[edit | edit source]
- Klitzing, Richard. "squacupe".