Small stellapentakis 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.

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

Proportions

The triangles have two acute angles of ${\displaystyle \arccos({\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 18.699\,407\,085\,149^{\circ }}$ and one obtuse angle of ${\displaystyle \arccos({\frac {1}{10}}-{\frac {2}{5}}{\sqrt {5}})\approx 142.601\,185\,829\,70^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos({\frac {-24-5{\sqrt {5}}}{41}})\approx 149.099\,125\,827\,35^{\circ }}$. 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, MR 0730208

External links

• Weisstein, Eric W. "Small stellapentakis dodecahedron". MathWorld.
• Uniform polyhedra and duals