Rotunda (geometry)


Set of rotundas
Pentagonal rotunda
(Example: pentagonal rotunda)
Faces 1 n-gon
1 2n-gon
n pentagons
2n triangles
Edges 7n
Vertices 4n
Symmetry group Cnv, [n], (*nn), order 2n
Rotation group Cn, [n]+, (nn), order n
Properties convex

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.

Other forms can be generated with dihedral symmetry and distorted equilateral pentagons.[example needed]

A square rotunda


3 4 5 6 7 8
triangular rotunda
square rotunda
pentagonal rotunda
hexagonal rotunda
heptagonal rotunda
octagonal rotunda


5 7 9 11
Pentagrammic rotunda
Heptagrammic rotunda
Enneagrammic rotunda
Hendecagrammic rotunda

See alsoEdit


  • Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. 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.