birotunda

{{Short description|Solid made from 2 rotunda joined base-to-base}}

{{Infobox polyhedron

| name = Set of cupolae

| image = Pentagonal orthobirotunda.png

| caption = Example: pentagonal orthobirotunda

| type =

| euler =

| faces = 2 {{mvar|n}}-gons
{{math|2n}} pentagons
{{math|4n}} triangles

| edges = {{math|12n}}

| vertices = {{math|6n}}

| vertex_config =

| schläfli =

| wythoff =

| conway =

| coxeter =

| symmetry = Ortho: {{math|Dihedral symmetry in three dimensions, [n,2], (*n22),}} order {{math|4n}}

Gyro: {{math|Dihedral symmetry in three dimensions, [2n,2{{sup|+ }}], (2*n),}} order {{math|4n}}

| rotation_group = {{math|D{{sub|n}}, [n,2]{{sup|+}}, (n22),}} order {{math|2n}}

| surface_area =

| volume =

| angle =

| dual =

| properties = convex

| vertex_figure =

| net =

| net_caption =

}}

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.