Great pentagrammic hexecontahedron

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.

Denote the golden ratio by

be the largest positive zero of the polynomial

Then each pentagrammic face has four equal angles of

arccos ⁡ ( ξ ) ≈ 18.785

Each face has three long and two short edges.

between the lengths of the long and the short edges is given by The dihedral angle equals

arccos ⁡ ( ξ

Part of each face lies inside the solid, hence is invisible in solid models.

play a similar role in the description of the great pentagonal hexecontahedron and the great inverted pentagonal hexecontahedron.

This polyhedron-related article is a stub.