Abstract regular polytopes

About “Abstract regular polytopes”

Abstract regular polytopes are the result of more than two millennia of geometrical research, beginning with regular polygons and polyhedra. They are highly symmetric structures with unique geometric, algebraic, and topological properties, offering greater fascination than traditional regular polytopes and tessellations. In the past 20 years, the subject has developed rapidly, creating a rich theory that connects geometry, combinatorics, group theory, and topology. This book is the first comprehensive and up-to-date account of abstract regular polytopes and their groups, addressing a critical need in the field. It fills a gap left since the publication of Coxeter's works in 1948 and 1974. The book is intended for researchers and graduate students in discrete geometry, combinatorics, and group theory.