Edges 50 Symmetry group C5v | Vertices 25 | |
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Type JohnsonJ32 - J33 - J34 Faces 3×5 triangles5 squares2+5 pentagons Vertex configuration 10(3.4.5)5(3.4.5.4)2.5(3.5.3.5) | ||
In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids (J33). Like the pentagonal orthocupolarotunda (J32), it can be constructed by joining a pentagonal cupola (J5) and a pentagonal rotunda (J6) along their decagonal bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.
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: