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In 
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a rotunda is any member of a family of dihedral-symmetric polyhedra
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
A convex polyhedron is the convex hull of finitely many points, not all on t ...
. They are similar to a cupola
In architecture, a cupola () is a relatively small, most often dome-like, tall structure on top of a building. Often used to provide a lookout or to admit light and air, it usually crowns a larger roof or dome.
The word derives, via Italian, from ...
but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. The pentagonal rotunda
In geometry, the pentagonal rotunda is one of the Johnson solids (). It can be seen as half of an icosidodecahedron, or as half of a pentagonal orthobirotunda. It has a total of 17 faces.
Formulae
The following formulae for volume, surface ar ...
is a Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...
.
Other forms can be generated with dihedral symmetry and distorted equilateral pentagons.
Examples
Star-rotunda
See also
*Birotunda
In geometry, a birotunda is any member of a family of dihedral-symmetric polyhedra, formed from two rotunda adjoined through the largest face. They are similar to a bicupola but instead of alternating squares and triangles, it alternates pent ...
References
*Norman W. Johnson
Norman Woodason Johnson () was a mathematician at Wheaton College, Norton, Massachusetts.
Early life and education
Norman Johnson was born on in Chicago. His father had a bookstore and published a local newspaper.
Johnson earned his unde ...
, "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.
* The first proof that there are only 92 Johnson solids.
{{Polyhedron navigator
Johnson solids