Great pentagrammic hexecontahedron
Introduction In geometry, the '''great pentagrammic hexecontahedron''' (or '''great dentoid ditriacontahedron''') is a nonconvex isohedral polyhedron. It is the dual of the great retrosnub icosidodecahedron. Its 60 faces are irregular pentagrams.3D model of a great pentagrammic hexecontahedron
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.
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