 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