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)
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

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

Examples

Rotundas

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

Star-rotunda

Star-rotundas

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

See also

• Birotunda

References

• 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.