Pentagonal orthocupolarotunda

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

$V=\frac{5}{12}(11+5\sqrt{5})a^3\approx 9.24181...a^3$

$A=(5+\frac{1}{4}\sqrt{1900+490\sqrt{5}+210\sqrt{75+30\sqrt{5}}})a^2\approx 23.5385...a^2$

External links

• Template:MathWorld2