small ditrigonal dodecacronic hexecontahedron

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

File:Small ditrigonal dodecacronic hexecontahedron.stl

In geometry, the small ditrigonal dodecacronic hexecontahedron (or fat star) is a nonconvex isohedral polyhedron. It is the dual of the uniform small ditrigonal dodecicosidodecahedron. It is visually identical to the small dodecicosacron. 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 $\arccos(\frac{5}{12}+\frac{1}{4}\sqrt{5})\approx 12.661\,078\,804\,43^{\circ}$ , one of $\arccos(-\frac{5}{12}-\frac{1}{60}\sqrt{5})\approx 116.996\,396\,851\,70^{\circ}$ and one of $360^{\circ}-\arccos(-\frac{1}{12}-\frac{19}{60}\sqrt{5})\approx 217.681\,445\,539\,45^{\circ}$ . Its dihedral angles equal $\arccos({\frac{-44-3\sqrt{5}}{61}})\approx 146.230\,659\,755\,53^{\circ}$ . 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 = SmallDitrigonalDodecacronicHexecontahedron| title =Small ditrigonal dodecacronic hexecontahedron}}

Category:Dual uniform polyhedra