Pentagonal orthobicupola

In geometry, the pentagonal orthobicupola is one of the Johnson solids (Template:Math). As the name suggests, it can be constructed by joining two pentagonal cupolae (Template:Math) along their decagonal bases, matching like faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola (Template:Math).

The pentagonal orthobicupola is the third in an infinite set of orthobicupolae.

Template:Johnson solid File:J30 pentagonal orthobicupola.stl

Formulae

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

$V=\frac{1}{3}(5+4\sqrt{5})a^3\approx \mathrm{4.64809...}{a}^3$

$A=(10+\sqrt{\frac{5}{2}(10+\sqrt{5}+\sqrt{75+30\sqrt{5}})})a^2\approx \mathrm{17.7711...}{a}^2$

External links

• Template:Mathworld2