In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola () by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae () through 36 degrees before inserting the prism yields an elongated pentagonal orthobicupola ().
thumb|3D model of an elongated pentagonal gyrobicupola
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:
:<math>V=\frac{1}{6}\left(10+8\sqrt{5}+15\sqrt{5+2\sqrt{5\right)a^3\approx12.3423...a^3</math>
:<math>A=\left(20+\sqrt{\frac{5}{2}\left(10+\sqrt{5}+\sqrt{75+30\sqrt{5\right)}\right)a^2\approx27.7711...a^2</math>