In geometry, the gyroelongated bicupolae are an infinite sets of polyhedra, constructed by adjoining two n-gonal cupolas to an n-gonal antiprism. The triangular, square, and pentagonal gyroelongated bicupola are three of five Johnson solids which are chiral, meaning that they have a "left-handed" and a "right-handed" form.
Adjoining two triangular prisms to a square antiprism also generates a polyhedron, but not a Johnson solid, as it is not convex. The hexagonal form is also a polygon, but has coplanar faces. Higher forms can be constructed without regular faces.
Image cwlaevo Image ccwdextro Name Faces Gyroelongated digonal bicupola 12 triangles, 4 squares Gyroelongated triangular bicupola (J44) 18+2 triangles, 6 squares Gyroelongated square bicupola (J45) 24 triangles, 8+2 squares Gyroelongated pentagonal bicupola (J46) 30 triangles, 10 squares, 2 pentagons Gyroelongated hexagonal bicupola 36 triangles, 12 squares, 2 hexagons
See also Elongated cupola Gyroelongated cupola Bicupola Elongated bicupola Rotunda
References Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others. The first proof that there are only 92 Johnson solids.