Small stellapentakis dodecahedron

The triangles have two acute angles of ${\displaystyle \arccos({\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 18.699\,407\,085\,149^{\circ }}$ and one obtuse angle of ${\displaystyle \arccos({\frac {1}{10}}-{\frac {2}{5}}{\sqrt {5}})\approx 142.601\,185\,829\,70^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos({\frac {-24-5{\sqrt {5}}}{41}})\approx 149.099\,125\,827\,35^{\circ }}$. Part of each triangle lies within the solid, hence is invisible in solid models.

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

• Weisstein, Eric W. "Small stellapentakis dodecahedron". MathWorld.
• Uniform polyhedra and duals