| Type: | Bicupola, Johnson |
| Faces: | 10 triangles 10 squares 2 pentagons |
| Edges: | 40 |
| Vertices: | 20 |
| Symmetry: | D5 |
| Vertex Config: | 10 x (3 x 4 x 3 x 4) 10 x (3 x 4 x 5 x 4) |
| Net: | Johnson solid 31 net.png |
The pentagonal gyrobicupola is a polyhedron that is constructed by attaching two pentagonal cupolas base-to-base, each of its cupolas is twisted at 36°. It is an example of a Johnson solid and a composite polyhedron.
The pentagonal gyrobicupola is a composite polyhedron: it is constructed by attaching two pentagonal cupolas base-to-base. This construction is similar to the pentagonal orthobicupola; the difference is that one of cupolas in the pentagonal gyrobicupola is twisted at 36°, as suggested by the prefix gyro-. The resulting polyhedron has the same faces as the pentagonal orthobicupola does: those cupolas cover their decagonal bases, replacing it with eight equilateral triangles, eight squares, and two regular pentagons. A convex polyhedron in which all of its faces are regular polygons is the Johnson solid. The pentagonal gyrobicupola has such these, enumerating it as the thirty-first Johnson solid
J31
Because it has a similar construction as the pentagonal orthobicupola, the surface area of a pentagonal gyrobicupola
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