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
Faces1 n-gon
1 2n-gon
n pentagons
2n triangles
Edges7n
Vertices4n
Symmetry groupCnv, [n], (*nn), order 2n
Rotation groupCn, [n]+, (nn), order n
Propertiesconvex

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

Examples

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

Star-rotunda

edit
Star-rotundas
5 7 9 11
 
Pentagrammic rotunda
 
Heptagrammic rotunda
 
Enneagrammic rotunda
 
Hendecagrammic rotunda

See also

edit

References

edit
  • 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.