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:
Deltoidal hexecontahedron - kitesPentagonal hexecontahedron - pentagonsTriakis icosahedron - isosceles trianglesPentakis dodecahedron - isosceles trianglesConcave
Rhombic hexecontahedron - rhombi27 uniform star-polyhedral duals: (self-intersecting)
Small dodecicosacron, Great dodecicosacronSmall rhombidodecacron, Great rhombidodecacronSmall dodecacronic hexecontahedron, Great dodecacronic hexecontahedronRhombicosacronSmall icosacronic hexecontahedron, Medial icosacronic hexecontahedron, Great icosacronic hexecontahedronSmall stellapentakis dodecahedron, Great stellapentakis dodecahedronGreat pentakis dodecahedronGreat triakis icosahedronSmall ditrigonal dodecacronic hexecontahedron, Great ditrigonal dodecacronic hexecontahedronMedial deltoidal hexecontahedron, Great deltoidal hexecontahedronMedial pentagonal hexecontahedron, Great pentagonal hexecontahedronMedial inverted pentagonal hexecontahedron, Great inverted pentagonal hexecontahedronGreat pentagrammic hexecontahedronSmall hexagonal hexecontahedron, Medial hexagonal hexecontahedron, Great hexagonal hexecontahedronSmall hexagrammic hexecontahedron
