Hendecagrammic prism

The four regular hendecagrams
{11/2}, {11/3}, {11/4}, and {11/5}

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.

Hendecagrammic prisms and bipyramids

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
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)




Hendecagrammic antiprisms

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
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

Hendecagrammic trapezohedra

The hendecagrammic trapezohedra are duals to the hendecagrammic antiprisms.

Symmetry Trapezohedra
D11h
[2,11]
(*2.2.11)



D11d
[2+,11]
(2*11)



See also

References

  1. Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.

External links

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