Gyroelongated pentagonal birotunda
In geometry, the gyroelongated pentagonal birotunda is one of the Johnson solids. As the name suggests, it can be constructed by gyroelongating a pentagonal birotunda 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, each bottom pentagon would be connected to a pentagonal face above it and to the right. The two chiral forms of are not considered different Johnson solids.
Area and volume
With edge length a, the surface area isand the volume is