Hendecagrammic prism
![](http://upload.wikimedia.org/wikipedia/commons/thumb/7/75/HendecagramTypes.png/220px-HendecagramTypes.png)
{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[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.
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]
- ^ 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.