Pentakis dodecahedron	Deltoidal hexecontahedron
Pentagonal hexecontahedron	Triakis icosahedron
Rhombic hexecontahedron	Small hexagonal hexecontahedron

In geometry, a hexecontahedron (or hexacontahedron^[1]) 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