In geometry, the gyroelongated pentagonal cupolarotunda is one of the

Johnson solid In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...

s (). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda ( or ) by inserting a decagonal antiprism between its two halves. The gyroelongated pentagonal cupolarotunda 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 square 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 square 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 is :

A=\frac\left(20+35\sqrt+7\sqrt\right)a^2\approx32.198786370...a^2,

and the volume is :

V=\left(\frac+\frac\sqrt+ \frac\sqrt\right) a^3\approx15.991096162...a^3.

External links

* {{Johnson solids navigator Johnson solids Chiral polyhedra