Hendecagrammic prism

Summary

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.

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

Hendecagrammic prisms and bipyramids edit

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 edit

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 edit

The hendecagrammic trapezohedra are duals to the hendecagrammic antiprisms.

Symmetry Trapezohedra
D11h
[2,11]
(*2.2.11)
 
       
 
       
 
       
D11d
[2+,11]
(2*11)
 
       
 
       
 
       

See also edit

References edit

  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.
  • Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954). "Uniform polyhedra". Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences. 246 (916). The Royal Society: 401–450. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446. S2CID 202575183.

External links edit