Hexecontahedron

In geometry, a hexecontahedron (or hexacontahedron ) is a polyhedron with 60 faces. There are many symmetric forms, and the ones with highest symmetry have icosahedral symmetry:

Four Catalan solids, convex:
 * Pentakis dodecahedron - isosceles triangles
 * Deltoidal hexecontahedron - kites
 * Pentagonal hexecontahedron - pentagons
 * Triakis icosahedron - isosceles triangles

Concave
 * Rhombic hexecontahedron - rhombi

27 uniform star-polyhedral duals: (self-intersecting)
 * Small dodecicosacron, Great dodecicosacron
 * Small rhombidodecacron, Great rhombidodecacron
 * Small dodecacronic hexecontahedron, Great dodecacronic hexecontahedron
 * Rhombicosacron
 * Small icosacronic hexecontahedron, Medial icosacronic hexecontahedron, Great icosacronic hexecontahedron
 * Small stellapentakis dodecahedron, Great stellapentakis dodecahedron
 * Great pentakis dodecahedron
 * Great triakis icosahedron
 * Small ditrigonal dodecacronic hexecontahedron, Great ditrigonal dodecacronic hexecontahedron
 * Medial deltoidal hexecontahedron, Great deltoidal hexecontahedron
 * Medial pentagonal hexecontahedron, Great pentagonal hexecontahedron
 * Medial inverted pentagonal hexecontahedron, Great inverted pentagonal hexecontahedron
 * Great pentagrammic hexecontahedron
 * Small hexagonal hexecontahedron, Medial hexagonal hexecontahedron, Great hexagonal hexecontahedron
 * Small hexagrammic hexecontahedron