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Polyhedra

Polyhedra Author Peter R. Cromwell
ISBN-10 0521664055
Release 1999-07-22
Pages 476
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This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics.



Convex Polyhedra

Convex Polyhedra Author A.D. Alexandrov
ISBN-10 9783540263401
Release 2006-03-30
Pages 542
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This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.



Polyhedron Models

Polyhedron Models Author Magnus J. Wenninger
ISBN-10 0521098599
Release 1974-04-26
Pages 208
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An explicit guide to the geometric principles, design, and construction of complex polyhedral figures



Polyhedra

Polyhedra Author Anthony Pugh
ISBN-10 0520030567
Release 1976-01-01
Pages 118
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Polyhedra has been writing in one form or another for most of life. You can find so many inspiration from Polyhedra also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Polyhedra book for free.



Integer Points in Polyhedra

Integer Points in Polyhedra Author Alexander Barvinok
ISBN-10 3037190523
Release 2008
Pages 189
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Integer Points in Polyhedra has been writing in one form or another for most of life. You can find so many inspiration from Integer Points in Polyhedra also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Integer Points in Polyhedra book for free.



Integral convex polyhedra and an approach to integralization

Integral convex polyhedra and an approach to integralization Author Murray Edelberg
ISBN-10 UCSD:31822011145729
Release 1970
Pages 170
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Many combinatorial optimization problems may be formulated as integer linear programming problems, that is, problems of the form: given a convex polyhedron P contained in the non-negative orthant of n-dimensional space, find an integer point in P which maximizes (or minimizes) a given linear objective function. Well known linear programming methods would suffice to solve such a problem if: (1) P is an integral convex polyhedron, or (2) P is transformed into the integral convex polyhedron that is the convex hull of the set of integer points in P, a process which is called integralization. This thesis provides some theoretical results concerning integral convex polyhedra and the process of integralization. Necessary and sufficient conditions for a convex polyhedron P to have the integral property are derived in terms of the system of linear inequalities defining P. A number-theoretic method for integralizing two-dimensional convex polyhedra is developed which makes use of a generalization of the division theorem for integers. The method is applicable to a restricted class of higher dimensional polyhedra as well. (Author).



Three Dimensional Nets and Polyhedra

Three Dimensional Nets and Polyhedra Author Alexander Frank Wells
ISBN-10 MINN:319510001661917
Release 1977-01-01
Pages 268
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Three Dimensional Nets and Polyhedra has been writing in one form or another for most of life. You can find so many inspiration from Three Dimensional Nets and Polyhedra also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Three Dimensional Nets and Polyhedra book for free.



A Plethora of Polyhedra in Origami

A Plethora of Polyhedra in Origami Author John Montroll
ISBN-10 0486422712
Release 2002
Pages 120
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Step-by-step instructions and 970 clear diagrams show beginning and experienced paperfolders how to create 27 amazing polyhedra from one sheet of paper. Graded according to difficulty, the projects range from a simple cube, tetrahedron and octahedron to a challenging rhombic dodecahedron, sunken icosahedron, and an antidiamond with pentagonal base.



A Geometric Analysis of the Platonic Solids and Other Semi Regular Polyhedra

A Geometric Analysis of the Platonic Solids and Other Semi Regular Polyhedra Author Kenneth J. M. MacLean
ISBN-10 9781932690996
Release 2007
Pages 153
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This book contains a meticulous geometric investigation of the five Platonic Solids and five other important polyhedra, as well as reference charts for each solid. (Mathematics)



Computer search for non isomorphic convex polyhedra

Computer search for non isomorphic convex polyhedra Author Donald W. Grace
ISBN-10 STANFORD:36105033224309
Release 1965
Pages 274
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To classify the polyhedra, to survey the polyhedral shapes, and to exhaust their variety by orderly enumeration is a naturally attractive problem, noticed by Euler and Jakob Steiner, to which some mathematicians, especially Max Bruckner, devoted considerable work. With the latest high-speed digital computers decades of manual labor can be compressed into hours. This dissertation is concerned with the solution of the enumeration problem on a digital computer. A tri- linear polyhedron is one in which each vertex is incident with exactly three edges. Two polyhedra are isomorphic if a one-toone correspondence can be established between the vertices, edges, and faces of one with those of the other, so that the incidence relations between elements are preserved. Two polyhedra are called equi-surrounded if a one-to-one correspondence can be established between the faces of one and the faces of the other so that each pair of corresponding faces has equivalent surroundings -- i. e. the neighbors of the two faces in question, when taken in cyclic order clockwise, display the same pattern of edge-counts. Isomorphism implies equisurroundedness. A counter-example with 18 faces disproves the converse. However, for polyhedra with up to 17 faces we can apparently equate isomorphism with equisurroundedness.



Descartes on Polyhedra

Descartes on Polyhedra Author P. J. Federico
ISBN-10 0387907602
Release 1982-12-01
Pages 145
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The present essay stems from a history of polyhedra from 1750 to 1866 written several years ago (as part of a more general work, not published). So many contradictory statements regarding a Descartes manuscript and Euler, by various mathematicians and historians of mathematics, were encountered that it was decided to write a separate study of the relevant part of the Descartes manuscript on polyhedra. The contemplated short paper grew in size, as only a detailed treatment could be of any value. After it was completed it became evident that the entire manuscript should be treated and the work grew some more. The result presented here is, I hope, a complete, accurate, and fair treatment of the entire manuscript. While some views and conclusions are expressed, this is only done with the facts before the reader, who may draw his or her own conclusions. I would like to express my appreciation to Professors H. S. M. Coxeter, Branko Griinbaum, Morris Kline, and Dr. Heinz-Jiirgen Hess for reading the manuscript and for their encouragement and suggestions. I am especially indebted to Dr. Hess, of the Leibniz-Archiv, for his assistance in connection with the manuscript. I have been greatly helped in preparing the translation ofthe manuscript by the collaboration of a Latin scholar, Mr. Alfredo DeBarbieri. The aid of librarians is indispensable, and I am indebted to a number of them, in this country and abroad, for locating material and supplying copies.



Convex polyhedra with regular faces

Convex polyhedra with regular faces Author Viktor A. Zalgaller
ISBN-10 UVA:X001456926
Release 1969
Pages 95
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Convex polyhedra with regular faces has been writing in one form or another for most of life. You can find so many inspiration from Convex polyhedra with regular faces also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Convex polyhedra with regular faces book for free.



Convex Polyhedra with Regularity Conditions and Hilbert s Third Problem

Convex Polyhedra with Regularity Conditions and Hilbert s Third Problem Author A. R. Rajwade
ISBN-10 8185931283
Release 2001-01
Pages 194
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Convex Polyhedra with Regularity Conditions and Hilbert s Third Problem has been writing in one form or another for most of life. You can find so many inspiration from Convex Polyhedra with Regularity Conditions and Hilbert s Third Problem also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Convex Polyhedra with Regularity Conditions and Hilbert s Third Problem book for free.



A Constellation of Origami Polyhedra

A Constellation of Origami Polyhedra Author John Montroll
ISBN-10 0486439585
Release 2004
Pages 120
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From the simple Triangular Diamond and the Tower to the more advanced Cuboctahedron and the magnificent Stella Octangular, 30 multifaceted marvels will not only challenge devotees of the ancient Japanese art of paperfolding but will also appeal to students and others interested in math and geometry.



Computing the Continuous Discretely

Computing the Continuous Discretely Author Matthias Beck
ISBN-10 9780387461120
Release 2007-11-27
Pages 227
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This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.



Multimodular Origami Polyhedra

Multimodular Origami Polyhedra Author Rona Gurkewitz
ISBN-10 9780486136776
Release 2012-03-08
Pages 80
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Explore the link between paperfolding and mathematics with this unique, well-illustrated guide to creating a world of multifaceted wonders that draws on elements of crystallography. Detailed instructions, clear diagrams.



Convex figures and polyhedra

Convex figures and polyhedra Author Lazarʹ Aronovich Li͡usternik
ISBN-10 STANFORD:36105033274064
Release 1963
Pages 176
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Convex figures and polyhedra has been writing in one form or another for most of life. You can find so many inspiration from Convex figures and polyhedra also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Convex figures and polyhedra book for free.