Great rhombidodecacron
# Great rhombidodecacron

Great rhombidodecacron :

| Type | Star polyhedron |
| - | - |
| Face | |
| Elements | F = 60, E = 120 V = 42 (χ = −18) |
| Symmetry group | $I_h,$ [5,3], *532 |
| Index references | $DU_{73}$ |
| dual polyhedron | Great rhombidodecahedron |

In geometry, the great rhombidodecacron (or Great dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the great rhombidodecahedron. It is visually identical to the great deltoidal hexecontahedron. Its faces are antiparallelograms.

## Proportions

Each antiparallelogram has two angles of $\arccos({\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 18.699\,407\,085\,15^{\circ }$ and two angles of $\arccos(-{\frac {5}{8}}+{\frac {1}{8}}{\sqrt {5}})\approx 110.211\,801\,805\,89^{\circ }$. The diagonals of each antiparallelogram intersect at an angle of $\arccos({\frac {1}{8}}+{\frac {9{\sqrt {5}}}{40}})\approx 51.088\,791\,108\,96^{\circ }$. The dihedral angle equals $\arccos({\frac {-19+8{\sqrt {5}}}{41}})\approx 91.553\,403\,672\,16^{\circ }$. The ratio between the lengths of the long edges and the short ones equals ${\frac {1}{2}}+{\frac {1}{2}}{\sqrt {5}}$, which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.

