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
D_11h [2,11] (*2.2.11)	4.4.11/2	4.4.11/3	4.4.11/4	4.4.11/5
D_11h [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
D_11h [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
D_11d [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
D_11h [2,11] (*2.2.11)
D_11d [2⁺,11] (2*11)

References[]

^ 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. The Royal Society. 246 (916): 401–450. doi:10.1098/rsta.1954.0003. ISSN 0080-4614. JSTOR 91532. MR 0062446. S2CID 202575183.

External links[]

Weisstein, Eric W. "Polygram". MathWorld.

[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.

[1]