Gyroelongated pentagonal bicupola

In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids (Template:Math). As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola (Template:Math or Template:Math) 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 Template:Math are not considered different Johnson solids.

Area and Volume

With edge length a, the surface area is

$A=\frac{1}{2}(20+15\sqrt{3}+\sqrt{25+10\sqrt{5}})a^2\approx 26.431335858...a^2,$

and the volume is

$V=(\frac{5}{3}+\frac{4}{3}\sqrt{5}+\frac{5}{6}\sqrt{2\sqrt{650+290\sqrt{5}}-2\sqrt{5}-2})a^3\approx 11.397378512...a^3.$

External links

• Template:Mathworld2