Tridyakis icosahedron
# Tridyakis icosahedron

Tridyakis icosahedron :

| Type | Star polyhedron |
| - | - |
| Face | |
| Elements | F = 120, E = 180 V = 44 (χ = −16) |
| Symmetry group | $I_h,$ [5,3], *532 |
| Index references | $DU_{45}$ |
| dual polyhedron | Icositruncated dodecadodecahedron |

In geometry, the tridyakis icosahedron is the dual polyhedron of the nonconvex uniform polyhedron, icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.

## Proportions

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

