In geometry, a hendecagrammic prism is a star polyhedron made from two identical regular hendecagrams connected by squares. The related hendecagrammic antiprisms are made from two identical regular hendecagrams connected by equilateral triangles.
There are 4 hendecagrammic uniform prisms, and 6 hendecagrammic uniform antiprisms. The prisms are constructed by 4.4.11/q vertex figures, Coxeter diagram. The hendecagrammic bipyramids, duals to the hendecagrammic prisms are also given.
Symmetry | Prisms | |||
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D11h [2,11] (*2.2.11) |
4.4.11/2 |
4.4.11/3 |
4.4.11/4 |
4.4.11/5 |
D11h [2,11] (*2.2.11) |
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The antiprisms with 3.3.3.3.11/q vertex figures, . Uniform antiprisms exist for p/q>3/2,[1] and are called crossed for p/q<2. For hendecagonal antiprism, two crossed antiprisms can not be constructed as uniform (with equilateral triangles): 11/8, and 11/9.
Symmetry | Antiprisms | Crossed- antiprisms | ||
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D11h [2,11] (*2.2.11) |
3.3.3.11/2 |
3.3.3.11/4 |
3.3.3.11/6 3.3.3.-11/5 |
Nonuniform 3.3.3.11/8 3.3.3.-11/3 |
D11d [2+,11] (2*11) |
3.3.3.11/3 |
3.3.3.11/5 |
3.3.3.11/7 3.3.3.-11/4 |
Nonuniform 3.3.3.11/9 3.3.3.-11/2 |
The hendecagrammic trapezohedra are duals to the hendecagrammic antiprisms.
Symmetry | Trapezohedra | ||
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D11h [2,11] (*2.2.11) |
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D11d [2+,11] (2*11) |
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