Great deltoidal hexecontahedron

Template:Uniform polyhedra db File:Great deltoidal hexecontahedron.stl In geometry, the great deltoidal hexecontahedron (or great sagittal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the nonconvex great rhombicosidodecahedron. It is visually identical to the great rhombidodecacron. It has 60 intersecting cross quadrilateral faces, 120 edges, and 62 vertices. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.

It is also called a great strombic hexecontahedron.

Proportions

The darts have two angles of $\arccos (\frac{1}{2}+\frac{1}{5}\sqrt{5})\approx 18.69940708515^{\circ }$, one of $\arccos (-\frac{1}{4}+\frac{1}{10}\sqrt{5})\approx 91.51239472074^{\circ }$ and one of $360^{\circ }-\arccos (-\frac{1}{8}-\frac{9}{40}\sqrt{5})\approx 231.08879110896^{\circ }$. The dihedral angle equals $\arccos (\frac{-19+8\sqrt{5}}{41})\approx 91.55340367216^{\circ }$. The ratio between the lengths of the long and short edges is $\frac{21+3\sqrt{5}}{22}\approx 1.25946381511$.

References

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External links

• Template:Mathworld
• Uniform polyhedra and duals

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