Great stellapentakis dodecahedron

In geometry, the great stellapentakis dodecahedron (or great astropentakis dodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the truncated great icosahedron. It has 60 intersecting triangular faces.

Great stellapentakis dodecahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 90 V = 32 (χ = 2)
Symmetry group	Ih, [5,3], *532
Index references	DU55
dual polyhedron	Truncated great icosahedron

3D model of a great stellapentakis dodecahedron

Proportions

The triangles have one angle of ${\displaystyle \arccos(-{\frac {7}{36}}-{\frac {1}{4}}{\sqrt {5}})\approx 138.891\,114\,686\,59^{\circ }}$ and two of ${\displaystyle \arccos({\frac {3}{4}}+{\frac {1}{12}}{\sqrt {5}})\approx 20.554\,442\,656\,71^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos({\frac {-80+9{\sqrt {5}}}{109}})\approx 123.320\,065\,258\,47^{\circ }}$. 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. "Great stellapentakis dodecahedron". MathWorld.
• Uniform polyhedra and duals