In geometry, the pentagonal rotunda is one of the Johnson solids (J6). It can be seen as half of an icosidodecahedron, or as half of a pentagonal orthobirotunda.
A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.
The following formulae for volume, surface area, circumradius, and height are valid if all faces are regular, with edge length a:
The dual of the pentagonal rotunda has 20 faces: 10 triangular, 5 rhombic, and 5 kites.
|Dual pentagonal rotunda
||Net of dual