Hexecontahedron

From HandWiki
Short description: Polyhedron with 60 faces
Pentakisdodecahedron.jpg
Pentakis dodecahedron
Deltoidalhexecontahedron.jpg
Deltoidal hexecontahedron
Pentagonalhexecontahedroncw.jpg
Pentagonal hexecontahedron
Triakisicosahedron.jpg
Triakis icosahedron
Rhombic hexecontahedron.png
Rhombic hexecontahedron
DU32 small hexagonal hexecontahedron.png
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:

Concave

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

References