Small stellapentakis dodecahedron

Short description: Polyhedron with 60 faces

Small stellapentakis dodecahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 90 V = 24 (χ = −6)
Symmetry group	Ih, [5,3], *532
Index references	DU37
dual polyhedron	Truncated great dodecahedron

In geometry, the small stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.

Proportions

The triangles have two acute angles of [math]\displaystyle{ \arccos(\frac{1}{2}+\frac{1}{5}\sqrt{5})\approx 18.699\,407\,085\,149^{\circ} }[/math] and one obtuse angle of [math]\displaystyle{ \arccos(\frac{1}{10}-\frac{2}{5}\sqrt{5})\approx 142.601\,185\,829\,70^{\circ} }[/math]. The dihedral angle equals [math]\displaystyle{ \arccos(\frac{-24-5\sqrt{5}}{41})\approx 149.099\,125\,827\,35^{\circ} }[/math]. Part of each triangle lies within the solid, hence is invisible in solid models.

References

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

External links

• Weisstein, Eric W.. "Small stellapentakis dodecahedron". http://mathworld.wolfram.com/SmallStellapentakisDodecahedron.html. 
• Uniform polyhedra and duals