Rotunda (geometry)

Summary

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

ExamplesEdit

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

Star-rotundaEdit

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

See alsoEdit

ReferencesEdit

  • 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.