In geometry, the elongated pentagonal orthobirotunda is one of the Johnson solids (). Its Conway polyhedron notation is at5jP5. As the name suggests, it can be constructed by elongating a pentagonal orthobirotunda () by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae () through 36 degrees before inserting the prism yields the elongated pentagonal gyrobirotunda ().
thumb|3D model of an elongated pentagonal orthobirotunda
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(45+17\sqrt{5}+15\sqrt{5+2\sqrt{5\right)a^3\approx21.5297...a^3</math>
:<math>A=\left(10+\sqrt{30\left(10+3\sqrt{5}+\sqrt{75+30\sqrt{5\right)}\right)a^2\approx39.306...a^2</math>