Edges 50 Symmetry group C5v | Vertices 25 | |
 | ||
Type Johnson
J31 - J32 - J33 Faces 3×5 triangles
5 squares
2+5 pentagons Vertex configuration 10(3.4.3.5)
5(3.4.5.4)
2.5(3.5.3.5) | ||
In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids (J32). As the name suggests, it can be constructed by joining a pentagonal cupola (J5) and a pentagonal rotunda (J6) along their decagonal bases, matching the pentagonal faces. A 36-degree rotation of one of the halves before the joining yields a pentagonal gyrocupolarotunda (J33).
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.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a: