Medial icosacronic hexecontahedron

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.

Medial icosacronic hexecontahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 44 (χ = −16)
Symmetry group	Ih, [5,3], *532
Index references	DU44
dual polyhedron	Icosidodecadodecahedron

3D model of a medial icosacronic hexecontahedron

Proportions

Faces have two angles of ${\displaystyle \arccos({\frac {3}{4}})\approx 41.409\,622\,109\,27^{\circ }}$, one of ${\displaystyle \arccos(-{\frac {1}{8}}+{\frac {7}{24}}{\sqrt {5}})\approx 58.184\,446\,117\,59^{\circ }}$ and one of ${\displaystyle 360^{\circ }-\arccos(-{\frac {1}{8}}-{\frac {7}{24}}{\sqrt {5}})\approx 218.996\,309\,663\,87^{\circ }}$. Its dihedral angles equal ${\displaystyle \arccos(-{\frac {5}{7}})\approx 135.584\,691\,402\,81^{\circ }}$. The ratio between the lengths of the long and short edges is ${\displaystyle {\frac {27+7{\sqrt {5}}}{22}}\approx 1.938\,748\,901\,93}$.

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links

• Weisstein, Eric W. "Medial icosacronic hexecontahedron". MathWorld.