# Rotunda (geometry)

In geometry, a **rotunda** is any member of a family of dihedral-symmetric polyhedra. They are similar to a cupola but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. The pentagonal rotunda is a Johnson solid.

Set of rotundas | |
---|---|

(Example: pentagonal rotunda) | |

Faces | 1 n-gons 1 2n-gons n pentagons2 n triangles |

Edges | 7n |

Vertices | 4n |

Symmetry group | C_{nv}, [n], (*nn), order 2n |

Rotation group | C_{n}, [n]^{+}, (nn), order n |

Properties | convex |

Other forms can be generated with dihedral symmetry and distorted equilateral pentagons.

## See also

## References

- Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics,
**18**, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others. - Victor A. Zalgaller (1969).
*Convex Polyhedra with Regular Faces*. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.

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