Elongated pentagonal gyrobicupola

In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids ($J38 – J39 – J40$). As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola ($D5d$) by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae ($20(3.43) 10(3.4.5.4)$) through 36 degrees before inserting the prism yields an elongated pentagonal orthobicupola ($J39$).

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


 * $$V=\frac{1}{6}\left(10+8\sqrt{5}+15\sqrt{5+2\sqrt{5}}\right)a^3\approx12.3423...a^3$$


 * $$A=\left(20+\sqrt{\frac{5}{2}\left(10+\sqrt{5}+\sqrt{75+30\sqrt{5}}\right)}\right)a^2\approx27.7711...a^2$$