The following formulae for volume, surface area, circumradius, and height are valid if all faces are regular, with edge length a:^[2]

${\displaystyle V=\left({\frac {1}{12}}\left(45+17{\sqrt {5}}\right)\right)a^{3}\approx 6.91776...a^{3}}$ 

${\displaystyle {\begin{aligned}A&=\left({\frac {1}{2}}{\sqrt {5\left(145+58{\sqrt {5}}+2{\sqrt {30\left(65+29{\sqrt {5}}\right)}}\right)}}\right)a^{2}\\&=\left({\frac {1}{2}}\left(5{\sqrt {3}}+{\sqrt {10\left(65+29{\sqrt {5}}\right)}}\right)\right)a^{2}\approx 22.3472...a^{2}\end{aligned}}}$ 

${\displaystyle R=\left({\frac {1}{2}}\left(1+{\sqrt {5}}\right)\right)a\approx 1.61803...a}$ 

${\displaystyle H=\left({\sqrt {1+{\frac {2}{\sqrt {5}}}}}\right)a\approx 1.37638...a}$ 

The dual of the pentagonal rotunda has 20 faces: 10 triangular, 5 rhombic, and 5 kites.

• Weisstein, Eric W., "Pentagonal rotunda" ("Johnson solid") at MathWorld.