Hexecontahedron
Polyhedron with 60 faces
 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
References
- ^ "Greek numerical prefixes".
- Weisstein, Eric W. "Hexecontahedron". MathWorld.
- v
- t
- e
Listed by number of faces and type
- Icositetrahedron (24)
- Triacontahedron (30)
- Icosidodecahedron (32)
- Hexoctahedron (48)
- Hexecontahedron (60)
- Enneacontahedron (90)
- Hectotriadiohedron (132)
- Apeirohedron (∞)
- face
- edge
- vertex
- uniform polyhedron (two infinite groups and 75)
- regular polyhedron (9)
- quasiregular polyhedron (16)
- semiregular polyhedron (two infinite groups and 50)
- Platonic solid (5)
- Archimedean solid (13)
- Catalan solid (13)
- Johnson solid (92)
- Kepler–Poinsot polyhedron (4)
- Star polyhedron (infinite)
- Uniform star polyhedron (57)
- prism
- antiprism
- frustum
- cupola
- wedge
- pyramid
- parallelepiped
