Medial icosacronic hexecontahedron
# Medial icosacronic hexecontahedron

Medial icosacronic hexecontahedron :

| Type | Star polyhedron |
| - | - |
| Face | |
| Elements | F = 60, E = 120 V = 44 (χ = −16) |
| Symmetry group | $I_h,$ [5,3], *532 |
| Index references | $DU_{44}$ |
| dual polyhedron | Icosidodecadodecahedron |

In geometry, the medial icosacronic hexecontahedron (or midly sagittal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform icosidodecadodecahedron. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.

## Proportions

Faces have two angles of $\arccos({\frac {3}{4}})\approx 41.409\,622\,109\,27^{\circ }$, one of $\arccos(-{\frac {1}{8}}+{\frac {7}{24}}{\sqrt {5}})\approx 58.184\,446\,117\,59^{\circ }$ and one of $360^{\circ }-\arccos(-{\frac {1}{8}}-{\frac {7}{24}}{\sqrt {5}})\approx 218.996\,309\,663\,87^{\circ }$. Its dihedral angles equal $\arccos(-{\frac {5}{7}})\approx 135.584\,691\,402\,81^{\circ }$. The ratio between the lengths of the long and short edges is ${\frac {27+7{\sqrt {5}}}{22}}\approx 1.938\,748\,901\,93$.

