Small rhombidodecacron

Small rhombidodecacron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 42 (χ = −18)
Symmetry group	Ih, [5,3], *532
Index references	DU39
dual polyhedron	Small rhombidodecahedron

In geometry, the small rhombidodecacron is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.

3D model of a small rhombidodecacron

Proportions

Each face has two angles of $\arccos({\frac {5}{8}}+{\frac {1}{8}}{\sqrt {5}})\approx 25.242\,832\,961\,52^{\circ }$ and two angles of $\arccos(-{\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 93.025\,844\,508\,96^{\circ }$. The diagonals of each antiparallelogram intersect at an angle of $\arccos({\frac {1}{4}}+{\frac {1}{10}}{\sqrt {5}})\approx 61.731\,322\,529\,52^{\circ }$. 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. The dihedral angle equals $\arccos({\frac {-19-8{\sqrt {5}}}{41}})\approx 154.121\,363\,125\,78^{\circ }$.

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links

• Weisstein, Eric W. "Small rhombidodecacron". MathWorld.
• Uniform polyhedra and duals