Elongated pentagonal gyrocupolarotunda

Template:Short description {{#invoke:Infobox|infobox}}Template:Template other

In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (Template:Math). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda (Template:Math) by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola (Template:Math) or the pentagonal rotunda (Template:Math) through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda (Template:Math).

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:<ref>Stephen Wolfram, "Elongated pentagonal gyrocupolarotunda" from Wolfram Alpha. Retrieved July 25, 2010.</ref>

<math>V=\frac{5}{12}\left(11+5\sqrt{5}+6\sqrt{5+2\sqrt{5}}\right)a^3\approx16.936...a^3</math>

<math>A=\frac{1}{4}\left(60+\sqrt{10\left(190+49\sqrt{5}+21\sqrt{75+30\sqrt{5}}\right)}\right)a^2\approx33.5385...a^2</math>

External links

• Template:Mathworld2