This is a completely new edition of the classic book which has been out of print for many years. The plans and illustrations of all 59 of the stellations of the icosahedron have been redrawn by Kate and David Krennell and there is a new introduction by Professor Coxeter. For a thorough understanding of the process of stellation and for splendid examples of polyhedra, this book will be a valuable addition to any mathematics library.