Medial icosacronic hexecontahedron

{{Short description|Polyhedron with 60 faces}}

{{Uniform polyhedra db|Uniform dual polyhedron stat table|IDD}}

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 41.409\,622\,109\,27^{\circ}, one of \arccos(-\frac{1}{8}+\frac{7}{24}\sqrt{5})\approx 58.184\,446\,117\,59^{\circ} and one of 360^{\circ}-\arccos(-\frac{1}{8}-\frac{7}{24}\sqrt{5})\approx 218.996\,309\,663\,87^{\circ}. Its dihedral angles equal \arccos(-\frac{5}{7})\approx 135.584\,691\,402\,81^{\circ}. The ratio between the lengths of the long and short edges is \frac{27+7\sqrt{5}}{22}\approx 1.938\,748\,901\,93.

References

  • {{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 |mr=730208 | year=1983}}