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Record Nr. |
UNINA9910817634003321 |
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Autore |
McMullen Peter <1942-> |
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Titolo |
Abstract regular polytopes / / Peter McMullen, Egon Schulte |
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Pubbl/distr/stampa |
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Cambridge ; ; New York, : Cambridge University Press, 2002 |
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ISBN |
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1-316-08575-9 |
0-511-54668-8 |
1-280-41990-3 |
9786610419906 |
0-511-16958-2 |
1-139-14822-2 |
0-511-06500-0 |
0-511-05867-5 |
0-511-30843-4 |
0-511-07346-1 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (xiii, 551 pages) : digital, PDF file(s) |
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Collana |
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Encyclopedia of mathematics and its applications |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
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Nota di bibliografia |
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Includes bibliographical references (p. 519-538) and indexes. |
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Nota di contenuto |
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; 1. Classical Regular Polytopes -- ; 2. Regular Polytopes -- ; 3. Coxeter Groups -- ; 4. Amalgamation -- ; 5. Realizations -- ; 6. Regular Polytopes on Space-Forms -- ; 7. Mixing -- ; 8. Twisting -- ; 9. Unitary Groups and Hermitian Forms -- ; 10. Locally Toroidal 4-Polytopes: I -- ; 11. Locally Toroidal 4-Polytopes: II -- ; 12. Higher Toroidal Polytopes -- ; 13. Regular Polytopes Related to Linear Groups -- ; 14. Miscellaneous Classes of Regular Polytopes. |
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Sommario/riassunto |
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Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations. The rapid development of the subject in the past 20 years has resulted in a rich new theory, featuring an attractive interplay of mathematical |
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areas, including geometry, combinatorics, group theory and topology. Abstract regular polytopes and their groups provide an appealing new approach to understanding geometric and combinatorial symmetry. This is the first comprehensive up-to-date account of the subject and its ramifications, and meets a critical need for such a text, because no book has been published in this area of classical and modern discrete geometry since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). The book should be of interest to researchers and graduate students in discrete geometry, combinatorics and group theory. |
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