Small rhombidodecacron

Template:Short description Template:Uniform polyhedra db File:Small rhombidodecacron.stl 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.

Proportions

Each face has two angles of $\arccos (\frac{5}{8}+\frac{1}{8}\sqrt{5})\approx 25.24283296152^{\circ }$ and two angles of $\arccos (-\frac{1}{2}+\frac{1}{5}\sqrt{5})\approx 93.02584450896^{\circ }$. The diagonals of each antiparallelogram intersect at an angle of $\arccos (\frac{1}{4}+\frac{1}{10}\sqrt{5})\approx 61.73132252952^{\circ }$. 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 $\arccos (\frac{-19-8\sqrt{5}}{41})\approx 154.12136312578^{\circ }$.

References

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External links

• Template:Mathworld
• Uniform polyhedra and duals

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