In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda () by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola () or the pentagonal rotunda () through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda ().
thumb|3D model of an elongated pentagonal gyrocupolarotunda
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}+6\sqrt{5+2\sqrt{5\right)a^3\approx16.936...a^3</math>
:<math>A=\frac{1}{4}\left(60+\sqrt{10\left(190+49\sqrt{5}+21\sqrt{75+30\sqrt{5\right)}\right)a^2\approx33.5385...a^2</math>