# Pentagrammic prism

In geometry, the **pentagrammic prism** is one in an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.

Uniform Pentagrammic prism | |
---|---|

Type | Prismatic uniform polyhedron |

Elements | F = 7, E = 15V = 10 (χ = 2) |

Faces by sides | 5{4}+2{^{5}/_{2}} |

Schläfli symbol | t{2,^{5}/_{2}} or {5/2}x{} |

Wythoff symbol | 2 ^{5}/_{2} | 2 |

Coxeter diagram | |

Symmetry | D_{5h}, [5,2], (*522), order 20 |

Rotation group | D_{5}, [5,2]^{+}, (522), order 10 |

Index references | U_{78(a)} |

Dual | Pentagrammic dipyramid |

Properties | nonconvex |

Vertex figure 4.4. ^{5}/_{2} |

It has 7 faces, 15 edges and 10 vertices. This polyhedron is identified with the indexed name U_{78} as a uniform polyhedron.

It is a special case of a right prism with a pentagram as base, which in general has rectangular non-base faces.

Note that the pentagram face has an ambiguous interior because it is self-intersecting. The central pentagon region can be considered interior or exterior depending on how interior is defined. One definition of interior is the set of points that have a ray that crosses the boundary an odd number of times to escape the perimeter.

In either case, it is best to show the pentagram boundary line to distinguish it from a concave decagon.

## Gallery

An alternative representation with hollow centers to the pentagrams. |
The pentagrammic dipyramid is the dual to the pentagrammic prism |

## External links

- Weisstein, Eric W. "Pentagrammic prism".
*MathWorld*. - Weisstein, Eric W. "Pentagrammic dipyramid".
*MathWorld*. - http://www.mathconsult.ch/showroom/unipoly/78.html
- http://bulatov.org/polyhedra/uniform/u03.html
- Paper model of pentagrammic prism
- https://web.archive.org/web/20050313234702/http://www.math.technion.ac.il/~rl/kaleido/data/03.html
- http://home.comcast.net/~tpgettys/nonconvexprisms.html
- https://web.archive.org/web/20060211140715/http://www.ac-noumea.nc/maths/amc/polyhedr/no_conv5_.htm
- Paper Model (net) Pentagrammic Prism