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Solids with full icosahedral symmetry
Platonic solids - regular polyhedra (all faces of the same type)
Contents
Archimedean solids - polyhedra with more than one polygon face type.
Catalan solids - duals of the Archimedean solids.
Chiral Archimedean and Catalan solids
Archimedean solids:
References
Solids with icosahedral symmetry Wikipedia(Text) CC BY-SA