great ditrigonal dodecacronic hexecontahedron

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File:Great ditrigonal dodecacronic hexecontahedron.stl

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

Proportions

Kite faces have two angles of $\arccos(\frac{5}{12}-\frac{1}{4}\sqrt{5})\approx 98.183\,872\,491\,81^{\circ}$ , one of $\arccos(-\frac{5}{12}+\frac{1}{60}\sqrt{5})\approx 112.296\,452\,073\,54^{\circ}$ and one of $\arccos(-\frac{1}{12}+\frac{19}{60}\sqrt{5})\approx 51.335\,802\,942\,83^{\circ}$ . Its dihedral angles equal $\arccos({\frac{-44+3\sqrt{5}}{61}})\approx 127.686\,523\,427\,48^{\circ}$ . The ratio between the lengths of the long edges and the short ones equals $\frac{31+5\sqrt{5}}{22}\approx 1.917\,288\,176\,70$ .

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}} p. 62

External links

{{mathworld | urlname = GreatDitrigonalDodecacronicHexecontahedron| title =Great ditrigonal dodecacronic hexecontahedron}}

Category:Dual uniform polyhedra