By Peter McMullen,Egon Schulte

summary average polytopes stand on the finish of greater than millennia of geometrical learn, which started with usual polygons and polyhedra. they're hugely symmetric combinatorial constructions with special geometric, algebraic or topological houses; in lots of methods extra interesting than conventional typical polytopes and tessellations. The speedy improvement of the topic long ago two decades has led to a wealthy new idea, that includes an enticing interaction of mathematical parts, together with geometry, combinatorics, workforce idea and topology. summary ordinary polytopes and their teams supply an beautiful new method of realizing geometric and combinatorial symmetry. this can be the 1st entire updated account of the topic and its ramifications, and meets a severe want for any such textual content, simply because no booklet has been released during this region of classical and glossy discrete geometry considering Coxeter's general Polytopes (1948) and average advanced Polytopes (1974). The publication may be of curiosity to researchers and graduate scholars in discrete geometry, combinatorics and staff theory.

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