Elongated pentagonal orthocupolarotunda

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

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:

$V=\frac{5}{12}(11+5\sqrt{5}+6\sqrt{5+2\sqrt{5}})a^3\approx 16.936...a^3$

$A=\frac{1}{4}(60+\sqrt{10(190+49\sqrt{5}+21\sqrt{75+30\sqrt{5}})})a^2\approx 33.5385...a^2$

External links

• Template:Mathworld2