Despite these positive reviews, Branko Grünbaum, himself an authority on geometric symmetry, is much less enthusiastic, writing that the book has "some serious shortcomings". These include the unnecessary use of "cute" neologisms for concepts that already have well-established terminology, an inadequate treatment of MacBeath's and Andreas Dress 's contributions to the book's notation, sloppy reasoning in some arguments, inaccurate claims of novelty and failure to credit previous work in the classification of colored plane patterns, missing cases in this classification, likely errors in other of the more technical parts, poor copyediting, and a lack of clear definitions that ends up leaving out such central notions as the symmetries of a circle without providing any explanation of why they were omitted.