Square-snub cubic duoprism
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| Square-snub cubic duoprism | |
|---|---|
| Rank | 5 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Squasnic |
| Coxeter diagram | x4o s4s3s |
| Elements | |
| Tera | 8+24 triangular-square duoprisms, 6 tesseracts, 4 snub cubic prisms |
| Cells | 32+96 cubes, 12+24+24+24 cubes, 4 snub cubes |
| Faces | 32+96 triangles, 24+24+48+96+96 squares |
| Edges | 48+96+96+96 |
| Vertices | 96 |
| Vertex figure | Mirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, √2 (base pentagon), √2 (top and side edges) |
| Measures (edge length 1) | |
| Circumradius | ≈ 1.51841 |
| Hypervolume | ≈ 7.88948 |
| Diteral angles | Tisdip–cube–tisdip: ≈ 153.23459° |
| Tisdip–cube–tes: ≈ 142.98343° | |
| Sniccup–snic–sniccup: 90° | |
| Tisdip–trip–sniccup: 90° | |
| Tes–cube–sniccup: 90° | |
| Height | 1 |
| Central density | 1 |
| Number of external pieces | 42 |
| Level of complexity | 50 |
| Related polytopes | |
| Army | Squasnic |
| Regiment | Squasnic |
| Dual | Square-pentagonal icositetrahedral duotegum |
| Conjugate | Square-snub cubic duoprism |
| Abstract & topological properties | |
| Euler characteristic | 2 |
| Orientable | Yes |
| Properties | |
| Symmetry | B3+×B2, order 192 |
| Convex | Yes |
| Nature | Tame |
The square-snub cubic duoprism or squasnic is a convex uniform duoprism that consists of 4 snub cubic prisms, 6 tesseracts, and 32 triangular-square duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-square duoprisms, and 1 tesseract. It is a duoprism based on a square and a snub cube, which makes it a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a square-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of:
where
![{\displaystyle c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0e053543245c7eb3c2fe252ebeaf90a41d5472)
![{\displaystyle c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7791d17422cd2a6303bb6d139195df532a19e75e)
![{\displaystyle c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89f699970f92e321dfbcfc179c55ecb2ae8fea77)
External links[edit | edit source]
- Klitzing, Richard. "squasnic".