Great icosacronic hexecontahedron

Template:Short description Template:Uniform polyhedra db File:Great icosacronic hexecontahedron.stl In geometry, the great icosacronic hexecontahedron (or great sagittal trisicosahedron) is the dual of the great icosicosidodecahedron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.

Proportions

Faces have two angles of $\arccos (\frac{3}{4}+\frac{1}{20}\sqrt{5})\approx 30.48032456536^{\circ }$, one of $\arccos (-\frac{1}{12}+\frac{19}{60}\sqrt{5})\approx 51.33580294283^{\circ }$ and one of $360^{\circ }-\arccos (-\frac{5}{12}+\frac{1}{60}\sqrt{5})\approx 247.70354792646^{\circ }$. Its dihedral angles equal $\arccos (\frac{-44+3\sqrt{5}}{61})\approx 127.68652342748^{\circ }$. The ratio between the lengths of the long and short edges is $\frac{31+5\sqrt{5}}{22}\approx 1.91728817670$.

References

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