Set of cupolae | |
---|---|

Faces | 2 n-gons 2 n pentagons4 n triangles |

Edges | 12n |

Vertices | 6n |

Symmetry group | Ortho: D_{nh}, [n,2], (*n22), order 4nGyro: D _{nd}, [2n,2^{+ }], (2*n), order 4n |

Rotation group | D_{n}, [n,2]^{+}, (n22), order 2n |

Properties | convex |

In geometry, a **birotunda** is any member of a family of dihedral-symmetric polyhedra, formed from two rotunda adjoined through the largest face. They are similar to a bicupola but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. There are two forms, *ortho-* and *gyro-*: an *orthobirotunda* has one of the two rotundas is placed as the mirror reflection of the other, while in a *gyrobirotunda* one rotunda is twisted relative to the other.

The pentagonal birotundas can be formed with regular faces, one a Johnson solid, the other a semiregular polyhedron:

- pentagonal orthobirotunda,
- pentagonal gyrobirotunda, which is also called an icosidodecahedron.

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

4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|

square orthobirotunda |
pentagonal orthobirotunda |
hexagonal orthobirotunda |
heptagonal orthobirotunda |
octagonal orthobirotunda |

square gyrobirotunda |
pentagonal gyrobirotunda (icosidodecahedron) |
hexagonal gyrobirotunda |
heptagonal gyrobirotunda |
octagonal gyrobirotunda |