Medial icosacronic hexecontahedron

Template:Short description Template:Uniform polyhedra db File:Medial icosacronic hexecontahedron.stl In geometry, the medial icosacronic hexecontahedron (or midly sagittal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform icosidodecadodecahedron. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.

Proportions

Faces have two angles of $\arccos (\frac{3}{4})\approx 41.40962210927^{\circ }$, one of $\arccos (-\frac{1}{8}+\frac{7}{24}\sqrt{5})\approx 58.18444611759^{\circ }$ and one of $360^{\circ }-\arccos (-\frac{1}{8}-\frac{7}{24}\sqrt{5})\approx 218.99630966387^{\circ }$. Its dihedral angles equal $\arccos (-\frac{5}{7})\approx 135.58469140281^{\circ }$. The ratio between the lengths of the long and short edges is $\frac{27+7\sqrt{5}}{22}\approx 1.93874890193$.

References

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External links

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