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 $\arccos (\frac{1}{2}+\frac{1}{5}\sqrt{5})\approx 18.699407085149^{\circ }$ and one obtuse angle of $\arccos (\frac{1}{10}-\frac{2}{5}\sqrt{5})\approx 142.60118582970^{\circ }$. The dihedral angle equals $\arccos (\frac{-24-5\sqrt{5}}{41})\approx 149.09912582735^{\circ }$. 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