Elongated pentagonal gyrobirotunda

In geometry, the elongated pentagonal gyrobirotunda or elongated icosidodecahedron is one of the Johnson solids ($J42 – J43 – J44$). As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron (one of the Archimedean solids), by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae ($D5d$) through 36 degrees before inserting the prism yields an elongated pentagonal orthobirotunda ($20(3.42.5) 2.10(3.5.3.5)$).

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


 * $$V=\frac{1}{6}\left(45+17\sqrt{5}+15\sqrt{5+2\sqrt{5}}\right)a^3 \approx 21.5297 a^3$$
 * $$A=\left(10+\sqrt{30\left(10+3\sqrt{5}+\sqrt{75+30\sqrt{5}}\right)}\right)a^2 \approx 39.306 a^2$$