Convex Polyhedra
Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive sour
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A.D. Alexandrov
Convex Polyhedra With 165 Figures
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† A.D. Alexandrov English translation by N.S. Dairbekov, S.S. Kutateladze and A.B. Sossinsky Comments and bibliography by V.A. Zalgaller Appendices by L.A. Shor and Yu. A. Volkov The Russian edition was published by Gosudarstv. Izdat. Tekhn.-Teor. Lit., Moscow-Leningrad, 1950
Library of Congress Control Number: 2004117404
Mathematics Subject Classification (2000): 52A99, 52B99 ISSN 1439-7382 ISBN 3-540-23158-7 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset by the authors using a Springer LATEX macro package Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper
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To Boris Nikolaevich Delaunay, my teacher
Preface to the English Translation
This book was published in Russian in 1950 [A16] and in German in 1958 [A19]. It continues the lines of the classical synthetic geometry in its subject and results. The methods are also synthetic and the book proves their might once again. Seemingly, this is why the book attracted a wide readership and gave an impetus to research for a few generations of mathematicians. In the intervening years, most problems that are listed in the book as unsolved were settled. Some results have acquired a more abstract and refined form or alternative proofs. In the present English edition, these changes are mainly commented in footnotes. The list of references is duly enlarged. The comments were made by V. A. Zalgaller on the author’s advice. The present edition includes the translations of two articles by Yu. A. Volkov and an article by L. A. Shor which present supplements to Chapters 3, 4, and 5. These are placed at the end of the book. The author is grateful to V. A. Zalgaller, who took pains to elaborate the present edition of the book, providing it with updating commentaries and references.
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Content and Purpose of the Book . . . . . . . . . .
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