Icositetrahedron
Polyhedron with 24 faces
 Triakis octahedron |  Tetrakis hexahedron |
 Deltoidal icositetrahedron |  Pentagonal icositetrahedron |
In geometry, an icositetrahedron[1] is a polyhedron with 24 faces. There are many symmetric forms, and the ones with highest symmetry have chiral icosahedral symmetry:
Four Catalan solids, convex:
- Triakis octahedron - isosceles triangles
- Tetrakis hexahedron - isosceles triangles
- Deltoidal icositetrahedron - kites
- Pentagonal icositetrahedron - pentagons
27 uniform star-polyhedral duals: (self-intersecting)
- Small rhombihexacron, Great rhombihexacron
- Small hexacronic icositetrahedron, Great hexacronic icositetrahedron
- Great deltoidal icositetrahedron
- Great triakis octahedron
References
- ^ "Greek numerical prefixes".
- Weisstein, Eric W. "Icositetrahedron". MathWorld.
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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
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