Great pentagrammic hexecontahedron
In geometry, the great pentagrammic hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the great retrosnub icosidodecahedron. Its 60 faces are irregular pentagrams.
Proportions
Denote the golden ratio by. Let be the largest positive zero of the polynomial. Then each pentagrammic face has four equal angles of and one angle of. Each face has three long and two short edges. The ratio between the lengths of the long and the short edges is given by
The dihedral angle equals. Part of each face lies inside the solid, hence is invisible in solid models. The other two zeroes of the polynomial play a similar role in the description of the great pentagonal hexecontahedron and the great inverted pentagonal hexecontahedron.
