Medial disdyakis triacontahedron

Medial disdyakis triacontahedron
Type	Star polyhedron
Face
Elements	F = 120, E = 180 V = 54 (χ = −6)
Symmetry group	Ih, [5,3], *532
Index references	DU59
dual polyhedron	Truncated dodecadodecahedron

In geometry, the medial disdyakis triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform truncated dodecadodecahedron. It has 120 triangular faces.

The triangles have one angle of ${\displaystyle \arccos(-{\frac {1}{10})\approx 95.739\,170\,477\,27^{\circ }$, one of ${\displaystyle \arccos({\frac {3}{8}+{\frac {11}{40}{\sqrt {5})\approx 8.142\,571\,179\,89^{\circ }$ and one of ${\displaystyle \arccos(-{\frac {3}{8}+{\frac {11}{40}{\sqrt {5})\approx 76.118\,258\,342\,85^{\circ }$. The dihedral angle equals ${\displaystyle \arccos(-{\frac {9}{11})\approx 144.903\,198\,772\,42^{\circ }$. 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. "Medial disdyakis triacontahedron". MathWorld.