Great dodecacronic hexecontahedron

File:Great dodecacronic hexecontahedron.stl

In geometry, the great dodecacronic hexecontahedron (or great lanceal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great dodecicosidodecahedron. Its 60 intersecting quadrilateral faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models.

Proportions

Each kite has two angles of $\arccos(\frac{5}{8}-\frac{1}{8}\sqrt{5})\approx 69.788\,198\,194\,11^{\circ}$ , one of $\arccos(-\frac{1}{4}+\frac{1}{10}\sqrt{5})\approx 91.512\,394\,720\,74^{\circ}$ and one of $\arccos(-\frac{1}{8}-\frac{9}{40}\sqrt{5})\approx 128.911\,208\,891\,04^{\circ}$ . The dihedral angle equals $\arccos(\frac{-19+8\sqrt{5}}{41})\approx 91.553\,403\,672\,16^{\circ}$ . The ratio between the lengths of the long and short edges is $\frac{21+3\sqrt{5}}{22}\approx 1.259\,463\,815\,11$ .

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 = GreatDodecacronicHexecontahedron| title =Great dodecacronic hexecontahedron}}

Category:Dual uniform polyhedra