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, fr ...

but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. The pentagonal rotunda 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 each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johns ...

. Other forms can be generated with dihedral symmetry and distorted equilateral pentagons. Square rotunda

Examples

Star-rotunda

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. * The first proof that there are only 92 Johnson solids. {{Polyhedron navigator Johnson solids

Examples

Star-rotunda

See also

References