Gyroelongated pentagonal rotunda

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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

<math>A=\frac{1}{2}\left( 15\sqrt{3}+\left(5+3\sqrt{5}\right)\sqrt{5+2\sqrt{5}}\right)a^2\approx31.007454303...a^2,</math>

and the volume is

<math>V=\left(\frac{45}{12}+\frac{17}{12}\sqrt{5} + \frac{5}{6}\sqrt{2\sqrt{650+290\sqrt{5}}-2\sqrt{5}-2}\right) a^3\approx13.667050844...a^3.</math>

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
File:Dual gyroelongated pentagonal rotunda.png	File:Dual gyroelongated pentagonal rotunda net.png

External links

• Template:Mathworld2