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