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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)

^ "Greek numerical prefixes".