title: Icositetrahedron
text: # Icositetrahedron
  
  | Triakis octahedron | Tetrakis hexahedron |
  | - | - |
  | Deltoidal icositetrahedron | Pentagonal icositetrahedron |
  
  In geometry, an icositetrahedron 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
  