Set of cupolae
Example: pentagonal orthobirotunda
Faces2 n-gons
2n pentagons
4n triangles
Edges12n
Vertices6n
Symmetry groupOrtho: Dnh, [n,2], (*n22), order 4n
Gyro: Dnd, [2n,2+ ], (2*n), order 4n
Rotation groupDn, [n,2]+, (n22), order 2n
Propertiesconvex

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:

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

## Examples

Birotundas
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