# Dodecagonal prism

In geometry, the **dodecagonal prism** is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.

Uniform Dodecagonal prism | |
---|---|

Type | Prismatic uniform polyhedron |

Elements | F = 14, E = 36, V = 24 (χ = 2) |

Faces by sides | 12{4}+2{12} |

Schläfli symbol | t{2,12} or {12}x{} |

Wythoff symbol | 2 12 | 2 2 2 6 | |

Coxeter diagrams | |

Symmetry | D_{12h}, [12,2], (*12.2.2), order 48 |

Rotation group | D_{12}, [12,2]^{+}, (12.2.2), order 24 |

References | U_{76(j)} |

Dual | Dodecagonal dipyramid |

Properties | convex, zonohedron |

Vertex figure 4.4.12 |

If faces are all regular, it is a semiregular polyhedron.

## Use

It is used in the construction of two prismatic uniform honeycombs:

Omnitruncated triangular-hexagonal prismatic honeycomb |
Truncated hexagonal prismatic honeycomb |

The new British one pound (£1) coin, which entered circulation in March 2017, is shaped like a dodecagonal prism.[1]

## Related polyhedra

Family of uniform prisms | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Polyhedron | |||||||||||

Coxeter | |||||||||||

Tiling | |||||||||||

Config. | 2.4.4 | 3.4.4 | 4.4.4 | 5.4.4 | 6.4.4 | 7.4.4 | 8.4.4 | 9.4.4 | 10.4.4 | 11.4.4 | 12.4.4 |

## References

- "New 12-sided pound coin to enter circulation in March".
*BBC News*. 2017-01-01. Retrieved 2017-04-20.

## External links

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