Rotunda (geometry)

In geometry, a rotunda is any member of a family of dihedral-symmetric polyhedra. They are similar to a cupola but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. The pentagonal rotunda is a Johnson solid.

Set of rotundas

(Example: pentagonal rotunda)
Faces1 n-gons
1 2n-gons
n pentagons
2n triangles
Symmetry groupCnv, [n], (*nn), order 2n
Rotation groupCn, [n]+, (nn), order n

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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