Edges 40 Symmetry group D5d | Vertices 20 | |
 | ||
Type Johnson
J30 - J31 - J32 Faces 10 triangles
10 squares
2 pentagons Vertex configuration 10(3.4.3.4)
10(3.4.5.4) | ||
In geometry, the pentagonal gyrobicupola is one of the Johnson solids (J31). Like the pentagonal orthobicupola (J30), it can be obtained by joining two pentagonal cupolae (J5) along their 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.
The pentagonal gyrobicupola is the third in an infinite set of gyrobicupolae.
The pentagonal gyrobicupola is what you get when you take a rhombicosidodecahedron, chop out the middle parabidiminished rhombicosidodecahedron (J80), and paste the two opposing cupolae back together.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a: