Birotunda

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In geometry, a birotunda is the name for several different polyhedra, formed from two rotundas adjoined through their common regular-decagon faces. In an orthobirotunda, 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. In addition, a rotunda may be elongated in various ways by a ring of faces that separates one rotunda from the other.

There are five birotundas among the Johnson solids:

• the pentagonal orthobirotunda,
• the pentagonal gyrobirotunda, more commonly called the icosidodecahedron,
• the elongated pentagonal orthobirotunda, in which a ring of ten square faces separates two mirrored rotundas,
• the elongated pentagonal gyrobirotunda, and
• the gyroelongated pentagonal birotunda, in which a ring of twenty triangular faces separates the two rotundas.

Another Johnson solid, the bilunabirotunda, is not a birotunda despite having that word as part of its name.