Great rhombidodecacron

Great rhombidodecacron
File:DU73 great rhombidodecacron.png
Type	Star polyhedron
Face	File:DU73 facets.png
Elements	F = 60, E = 120 V = 42 (χ = −18)
Symmetry group	Ih, [5,3], *532
Index references	DU73
dual polyhedron	Great rhombidodecahedron

File:Great rhombidodecacron.stl

3D model of a great rhombidodecacron

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 $\arccos (\frac{1}{2}+\frac{1}{5}\sqrt{5})\approx 18.69940708515^{\circ }$ and two angles of $\arccos (-\frac{5}{8}+\frac{1}{8}\sqrt{5})\approx 110.21180180589^{\circ }$. The diagonals of each antiparallelogram intersect at an angle of $\arccos (\frac{1}{8}+\frac{9\sqrt{5}}{40})\approx 51.08879110896^{\circ }$. The dihedral angle equals $\arccos (\frac{-19+8\sqrt{5}}{41})\approx 91.55340367216^{\circ }$. 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.

References

• p. 88