| Gyroelongated pentagonal birotunda | |
|---|---|
| Type | Johnson J47 - J48 - J49 |
| Faces | 4x10 triangles 2+10 pentagons |
| Edges | 90 |
| Vertices | 40 |
| Vertex configuration | 2x10(3.5.3.5) 2.10(34.5) |
| Symmetry group | D5 |
| Dual polyhedron | - |
| Properties | convex, chiral |
| Net | |
In geometry, the gyroelongated pentagonal birotunda is one of the Johnson solids (J48). As the name suggests, it can be constructed by gyroelongating a pentagonal birotunda (either J34 or the icosidodecahedron) by inserting a decagonal antiprism between its two halves.
The gyroelongated pentagonal birotunda 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 pentagonal face on the bottom half of the figure is connected by a path of two triangular faces to a pentagonal face above it and to the left. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom pentagon would be connected to a pentagonal face above it and to the right. The two chiral forms of J48 are not considered different Johnson solids.
The 92 Johnson solids were named and described by Norman Johnson in 1966.