What is a sixty faced polyhedron called?

A sixty-faced polyhedron is known as a hexacontahedron. Specifically, one of the most common types is the hexacontahedron with regular hexagonal faces, which is referred to as a regular hexacontahedron or a hexagonal bipyramid. There are various other configurations of sixty-faced polyhedra as well, but they all fall under the broader category of hexacontahedra.