Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. The rapid development of the subject in the past twenty years has resulted in a rich new theory featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. This is the first comprehensive, up-to-date account of the subject and its ramifications. It meets a critical need for such a text, because no book has been published in this area since Coxeter's "Regular Polytopes" (1948) and "Regular Complex Polytopes" (1974).

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Abstract regular polytopes are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties. This comprehensive up-to-date account of the subject meets a critical need for a text in this area; no book has been published in this topic since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974).

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