Hendecagrammic prism
# Hendecagrammic prism

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 | Prisms | Prisms | 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, 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 | Antiprisms | Crossed- 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 | Trapezohedra | Trapezohedra |
| - | - | - | - |
| $D_{11h}$ [2,11] (*2.2.11) | | | |
| $D_{11d}$ $[2^+,11]$ (2*11) | | | |
