Medial disdyakis triacontahedron
# Medial disdyakis triacontahedron

Medial disdyakis triacontahedron :

| Type | Star polyhedron |
| - | - |
| Face | |
| Elements | F = 120, E = 180 V = 54 (χ = −6) |
| Symmetry group | $I_h,$ [5,3], *532 |
| Index references | $DU_{59}$ |
| 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.

## Proportions

The triangles have one angle of $\arccos(-{\frac {1}{10}})\approx 95.739\,170\,477\,27^{\circ }$, one of $\arccos({\frac {3}{8}}+{\frac {11}{40}}{\sqrt {5}})\approx 8.142\,571\,179\,89^{\circ }$ and one of $\arccos(-{\frac {3}{8}}+{\frac {11}{40}}{\sqrt {5}})\approx 76.118\,258\,342\,85^{\circ }$. The dihedral angle equals $\arccos(-{\frac {9}{11}})\approx 144.903\,198\,772\,42^{\circ }$. Part of each triangle lies within the solid, hence is invisible in solid models.

