In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by joining a pentagonal cupola () and a pentagonal rotunda () along their decagonal bases, matching the pentagonal faces. A 36-degree rotation of one of the halves before the joining yields a pentagonal gyrocupolarotunda ().
thumb|3D model of a pentagonal orthocupolarotunda
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:
:<math>V=\frac{5}{12}\left(11+5\sqrt{5}\right)a^3\approx9.24181...a^3</math>
:<math>A=\left(5+\frac{1}{4}\sqrt{1900+490\sqrt{5}+210\sqrt{75+30\sqrt{5}\right)a^2\approx23.5385...a^2</math>