Square-icosahedral duoprism
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Square-icosahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Squike |
Coxeter diagram | x4o o5o3x |
Elements | |
Tera | 20 triangular-square duoprisms, 4 icosahedral prisms |
Cells | 80 triangular prisms, 30 cubes, 4 icosahedra |
Faces | 80 triangles, 12+120 squares |
Edges | 48+120 |
Vertices | 48 |
Vertex figure | Pentagonal scalene, edge lengths 1 (base pentagon) √2 (top and sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tisdip–cube–tisdip: |
Ipe–ike–ipe: 90° | |
Tisdip–trip–ipe: 90° | |
Height | 1 |
Central density | 1 |
Number of external pieces | 24 |
Level of complexity | 10 |
Related polytopes | |
Army | Squike |
Regiment | Squike |
Dual | Square-dodecahedral duotegum |
Conjugate | Square-great icosahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | H3×B2, order 960 |
Convex | Yes |
Nature | Tame |
The square-icosahedral duoprism or squike is a convex uniform duoprism that consists of 4 icosahedral prisms and 20 triangular-square duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-square duoprisms. It is a duoprism based on a square and an icosahedron, which makes it a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a square-icosahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
Representations[edit | edit source]
A square-icosahedral duoprism has the following Coxeter diagrams:
- x4o o5o3x (full symmetry)
- x x o5o3x (icosahedral prismatic prism)
External links[edit | edit source]
- Klitzing, Richard. "squike".