| Gyroelongated pentagonal bicupola | |
|---|---|
 | |
| Type | Johnson J45 – J46 – J47 |
| Faces | 30 triangles 10 squares 2 pentagons |
| Edges | 70 |
| Vertices | 30 |
| Vertex configuration | 10(3.4.5.4) 2.10(34.4) |
| Symmetry group | D5 |
| Dual polyhedron | - |
| Properties | convex, chiral |
| Net | |
 | |
In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids (J46). As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola ( J30 or J31 ) by inserting a decagonal antiprism between its congruent halves.
The gyroelongated pentagonal bicupola is one of five Johnson solids which are chiral, meaning that they have a "left-handed" and a "right-handed" form. In the illustration to the right, each square face on the bottom half of the figure is connected by a path of two triangular faces to a square face above it and to the right. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom square would be connected to a square face above it and to the left. The two chiral forms of J46 are not considered different Johnson solids.
A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (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. [1]
