[3] Reviewer Bill Casselman writes that it would probably not be appropriate to use as a textbook in this area, but could be valuable as additional reference material for an undergraduate geometry class.
[5] Despite complaints about vague referencing of its sources and credits for its historical images, missed connections to modern work in group theory, difficult-to-follow proofs, and occasionally-clumsy illustrations, and typographical errors, Casselman also reviews the book positively, calling it "valuable and a labor of love".
However, two experts on the topics of the book who also reviewed it, polyhedral combinatorics specialist Peter McMullen and historian of mathematics Judith Grabiner, were much less positive.
[6] And Grabiner faults the book's history as naive or mistaken, citing as examples its claims that the discovery of irrational numbers ended Pythagorean mysticism, and that pre-Keplerian astronomy consisted only of observation and record-keeping.
She writes that the book can be enjoyed as "a treasury" of "beautiful models" and "examples of the impact of polyhedra on the imagination of artists" but should not be relied on for historical insights.