Great ditrigonal dodecacronic hexecontahedron

Kite faces have two angles of ${\displaystyle \arccos({\frac {5}{12}}-{\frac {1}{4}}{\sqrt {5}})\approx 98.183\,872\,491\,81^{\circ }}$, one of ${\displaystyle \arccos(-{\frac {5}{12}}+{\frac {1}{60}}{\sqrt {5}})\approx 112.296\,452\,073\,54^{\circ }}$ and one of ${\displaystyle \arccos(-{\frac {1}{12}}+{\frac {19}{60}}{\sqrt {5}})\approx 51.335\,802\,942\,83^{\circ }}$. Its dihedral angles equal ${\displaystyle \arccos({\frac {-44+3{\sqrt {5}}}{61}})\approx 127.686\,523\,427\,48^{\circ }}$. The ratio between the lengths of the long edges and the short ones equals ${\displaystyle {\frac {31+5{\sqrt {5}}}{22}}\approx 1.917\,288\,176\,70}$.

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208 p. 62

• Weisstein, Eric W. "Great ditrigonal dodecacronic hexecontahedron". MathWorld.

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