| Type: | Johnson |
| Faces: | 3.10 triangles 10 squares 2 pentagons |
| Edges: | 70 |
| Vertices: | 30 |
| Dual: | - |
| Properties: | convex, chiral |
| Net: | Johnson solid 46 net.png |
In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids . As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola (or) 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 are not considered different Johnson solids.
With edge length a, the surface area is
| A= | 1 |
| 2 |
\left(20+15\sqrt{3}+\sqrt{25+10\sqrt{5}}\right)a2 ≈ 26.431335858...a2,
and the volume is
| V=\left( | 5 | + |
| 3 |
| 4 | |
| 3 |
\sqrt{5}+
| 5 | |
| 6 |
\sqrt{2\sqrt{650+290\sqrt{5}}-2\sqrt{5}-2}\right)a3 ≈ 11.397378512...a3.