Elongated pentagonal orthobirotunda

In geometry, the elongated pentagonal orthobirotunda is one of the Johnson solids (Template:Math). Its Conway polyhedron notation is at5jP5. As the name suggests, it can be constructed by elongating a pentagonal orthobirotunda (Template:Math) by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae (Template:Math) through 36 degrees before inserting the prism yields the elongated pentagonal gyrobirotunda (Template:Math).

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:^[1]

V = \frac{1}{6} (45 + 17 \sqrt{5} + 15 \sqrt{5 + 2 \sqrt{5}}) a^{3} \approx 21.5297 . . . a^{3}

A = (10 + \sqrt{30 (10 + 3 \sqrt{5} + \sqrt{75 + 30 \sqrt{5}})}) a^{2} \approx 39.306 . . . a^{2}