Hendecagonal-snub cubic duoprism
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Hendecagonal-snub cubic duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Hensnic |
Coxeter diagram | x11o s4s3s |
Elements | |
Tera | 8+24 triangular-hendecagonal duoprisms, 6 square-hendecagonal duoprisms, 11 snub cubic prisms |
Cells | 88+264 triangular prisms, 66 cubes, 12+24+24 hendecagonal prisms, 11 snub cubes |
Faces | 88+264 triangles, 66+132+264+264 squares, 24 hendecagons |
Edges | 132+264+264+264 |
Vertices | 264 |
Vertex figure | Mirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, √2 (base pentagon), 2cos(π/11) (top edge), √2 (side edges) |
Measures (edge length 1) | |
Circumradius | ≈ 2.22604 |
Hypervolume | ≈ 73.89003 |
Diteral angles | Thendip–henp–thendip: ≈ 153.23459° |
Sniccup–snic–sniccup: | |
Thendip–henp–shendip: ≈ 142.98343° | |
Thendip–trip–sniccup: 90° | |
Shendip–cube–sniccup: 90° | |
Central density | 1 |
Number of external pieces | 49 |
Level of complexity | 50 |
Related polytopes | |
Army | Hensnic |
Regiment | Hensnic |
Dual | Hendecagonal-pentagonal icositetrahedral duotegum |
Conjugates | Small hendecagrammic-snub cubic duoprism, Hendecagrammic-snub cubic duoprism, Great hendecagrammic-snub cubic duoprism, Grand hendecagrammic-snub cubic duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B3+×I2(11), order 528 |
Convex | Yes |
Nature | Tame |
The hendecagonal-snub cubic duoprism or hensnic is a convex uniform duoprism that consists of 11 snub cubic prisms, 6 square-hendecagonal duoprisms, and 32 triangular-hendecagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-hendecagonal duoprisms, and 1 square-hendecagonal duoprism.
Vertex coordinates[edit | edit source]
The vertices of a hendecagonal-snub cubic duoprism of edge length 2sin(π/11) 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
- j = 2, 4, 6, 8, 10,