Great stellapentakis dodecahedron
# Great stellapentakis dodecahedron

Great stellapentakis dodecahedron :

| Type | Star polyhedron |
| - | - |
| Face | |
| Elements | F = 60, E = 90 V = 32 (χ = 2) |
| Symmetry group | $I_h,$ [5,3], *532 |
| Index references | $DU_{55}$ |
| dual polyhedron | Truncated great icosahedron |

In geometry, the great stellapentakis dodecahedron (or great astropentakis dodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the truncated great icosahedron. It has 60 intersecting triangular faces.

## Proportions

The triangles have one angle of $\arccos(-{\frac {7}{36}}-{\frac {1}{4}}{\sqrt {5}})\approx 138.891\,114\,686\,59^{\circ }$ and two of $\arccos({\frac {3}{4}}+{\frac {1}{12}}{\sqrt {5}})\approx 20.554\,442\,656\,71^{\circ }$. The dihedral angle equals $\arccos({\frac {-80+9{\sqrt {5}}}{109}})\approx 123.320\,065\,258\,47^{\circ }$. Part of each triangle lies within the solid, hence is invisible in solid models.

