Elongated pentagonal orthobicupola

In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids (Template:Math). As the name suggests, it can be constructed by elongating a pentagonal orthobicupola (Template:Math) by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an elongated pentagonal gyrobicupola (Template:Math).

Formulae

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

$V=\frac{1}{6}(10+8\sqrt{5}+15\sqrt{5+2\sqrt{5}})a^3\approx 12.3423...a^3$

$A=(20+\sqrt{\frac{5}{2}(10+\sqrt{5}+\sqrt{75+30\sqrt{5}})})a^2\approx 27.7711...a^2$

External links

• Template:Mathworld2