Tridyakis icosahedron

The triangles have one angle of ${\displaystyle \arccos({\frac {3}{5}})\approx 53.130\,102\,354\,16^{\circ }}$, one of ${\displaystyle \arccos({\frac {1}{3}}+{\frac {4}{15}}{\sqrt {5}})\approx 21.624\,633\,927\,143^{\circ }}$ and one of ${\displaystyle \arccos({\frac {1}{3}}-{\frac {4}{15}}{\sqrt {5}})\approx 105.245\,263\,718\,70^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos(-{\frac {7}{8}})\approx 151.044\,975\,628\,14^{\circ }}$. Part of each triangle lies within the solid, hence is invisible in solid models.

• Catalan solid Duals to convex uniform polyhedra
• Uniform polyhedra
• List of uniform polyhedra

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208 Photo on page 96, Dorman Luke construction and stellation pattern on page 97.
• Weisstein, Eric W. "Tridyakis Icosahedron". MathWorld.

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