Gyroelongated pentagonal rotunda

In geometry, the gyroelongated pentagonal rotunda is one of the Johnson solids (J₂₅). As the name suggests, it can be constructed by gyroelongating a pentagonal rotunda (J₆) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal birotunda (J₄₈) with one pentagonal rotunda removed.

Area and Volume

With edge length a, the surface area is

$A=\frac{1}{2}(15\sqrt{3}+(5+3\sqrt{5})\sqrt{5+2\sqrt{5}})a^2\approx 31.007454303...a^2,$

and the volume is

$V=(\frac{45}{12}+\frac{17}{12}\sqrt{5}+\frac{5}{6}\sqrt{2\sqrt{650+290\sqrt{5}}-2\sqrt{5}-2})a^3\approx 13.667050844...a^3.$

Dual polyhedron

The dual of the gyroelongated pentagonal rotunda has 30 faces: 10 pentagons, 10 rhombi, and 10 quadrilaterals.

Dual gyroelongated pentagonal rotunda	Net of dual

External links

• Template:Mathworld2