The pentagonal gyrobicupola is a polyhedron that is constructed by attaching two pentagonal cupolas base-to-base, each of its cupolas is twisted at 36ð. 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 the cupolas in the pentagonal gyrobicupola is twisted at 36ð, 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 them with ten equilateral triangles, ten 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 these, enumerating it as the thirty-first Johnson solid .
The surface area of a pentagonal gyrobicupola is the sum of its faces' area, and its volume is twice the volume of a pentagonal cupola:
The pentagonal gyrobicupola has a three-dimensional symmetry group, the antiprismatic symmetry of . Its dihedral angles (i.e., the angle between two adjacent polygonal faces) are as follows: