Small icosacronic hexecontahedron

File:Small icosacronic hexecontahedron.stl

In geometry, the small icosacronic hexecontahedron (or small lanceal trisicosahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform small icosicosidodecahedron. Its faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models.

Proportions

The kites have two angles of $\arccos(\frac{3}{4}-\frac{1}{20}\sqrt{5})\approx 50.342\,524\,343\,87^{\circ}$ , one of $\arccos(-\frac{1}{12}-\frac{19}{60}\sqrt{5})\approx 142.318\,554\,460\,55^{\circ}$ and one of $\arccos(-\frac{5}{12}-\frac{1}{60}\sqrt{5})\approx 116.996\,396\,851\,70^{\circ}$ . The dihedral angle equals $\arccos(\frac{-44-3\sqrt{5}}{61})\approx 146.230\,659\,755\,53^{\circ}$ . The ratio between the lengths of the long and short edges is $\frac{31+5\sqrt{5}}{38}\approx 1.110\,008\,944\,41$ .

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}}

External links

{{mathworld | urlname = SmallIcosacronicHexecontahedron| title =Small icosacronic hexecontahedron}}

Category:Dual uniform polyhedra