Elongated pentagonal orthocupolarotunda

In geometry, the elongated pentagonal orthocupolarotunda is one of the Johnson solids ($J39 – J40 – J41$). As the name suggests, it can be constructed by elongating a pentagonal orthocupolarotunda ($C5v$) by inserting a decagonal prism between its halves. Rotating either the cupola or the rotunda through 36 degrees before inserting the prism yields an elongated pentagonal gyrocupolarotunda ($10(3.43) 10(3.42.5) 5(3.4.5.4) 2.5(3.5.3.5)$).

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


 * $$V=\frac{5}{12}\left(11+5\sqrt{5}+6\sqrt{5+2\sqrt{5}}\right)a^3\approx16.936...a^3$$


 * $$A=\frac{1}{4}\left(60+\sqrt{10\left(190+49\sqrt{5}+21\sqrt{75+30\sqrt{5}}\right)}\right)a^2\approx33.5385...a^2$$