Small dodecicosacron

Each face has two angles of ${\displaystyle \arccos({\frac {5}{12}}+{\frac {1}{4}}{\sqrt {5}})\approx 12.661\,078\,804\,43^{\circ }}$ and two angles of ${\displaystyle \arccos(-{\frac {3}{4}}+{\frac {1}{20}}{\sqrt {5}})\approx 129.657\,475\,656\,13^{\circ }}$ . The diagonals of each antiparallelogram intersect at an angle of ${\displaystyle \arccos({\frac {1}{12}}+{\frac {19}{60}}{\sqrt {5}})\approx 37.681\,445\,539\,45^{\circ }}$ . The dihedral angle equals ${\displaystyle \arccos({\frac {-44-3{\sqrt {5}}}{61}})\approx 146.230\,659\,755\,53^{\circ }}$ . The ratio between the lengths of the long edges and the short ones equals ${\displaystyle {\frac {1}{2}}+{\frac {1}{2}}{\sqrt {5}}}$ , which is the golden ratio. Part of each face lies inside 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 dodecicosacron". MathWorld.

• Uniform polyhedra and duals