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.

Set of birotundas

(Example Ortho/gyro pentagonal forms)
Faces2 n-gons
2n pentagons
4n triangles
Symmetry groupOrtho: Dnh, [n,2], (*n22), order 4n

Gyro: Dnd, [2n,2+], (2*n), order 4n

Rotation groupDn, [n,2]+, (n22), order 2n

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.

See also


  • Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169200. 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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