Search results for: polyhedra

Polyhedra

Author : Peter R. Cromwell
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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.

Polyhedra

Author : Anthony Pugh
File Size : 69.68 MB
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Convex Polyhedra

Author : A.D. Alexandrov
File Size : 43.16 MB
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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.

A Constellation of Origami Polyhedra

Author : John Montroll
File Size : 52.88 MB
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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.

Integer Points in Polyhedra

Author : Alexander Barvinok
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This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra-Lenstra-Lovasz lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.

Descartes on Polyhedra

Author : P. J. Federico
File Size : 73.46 MB
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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.

Multimodular Origami Polyhedra

Author : Rona Gurkewitz
File Size : 63.80 MB
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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.

Origami Polyhedra Design

Author : John Montroll
File Size : 60.22 MB
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This book unravels the mystery of Geometry in Origami with a unique approach: 64 Polyhedra designs, each made from a single square sheet of paper, no cuts, no glue; each polyhedron the largest possible from the starting size of square and each having an ingenious locking mechanism to hold its shape. The author covers the five Platonic solids (cube, tetrahedron, octahedron, icosahedron and dodecahedron). There are ample variations with different color patterns and sunken sides. Dipyramids and Dimpled Dipyramids, unexplored before this in Origami, are also covered. There are a total of 64 models in the book. All the designs have an interesting look and a pleasing folding sequence and are based on unique mathematical equations.

Harmonic Maps Between Riemannian Polyhedra

Author : J. Eells
File Size : 31.39 MB
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A research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.

Beginner s Book of Modular Origami Polyhedra

Author : Rona Gurkewitz
File Size : 26.51 MB
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This manual features 17 easy-to-master projects involving the Platonic solids: the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Includes detailed diagrams and photos of all the completed models.

Modular Origami Polyhedra

Author : Lewis Simon
File Size : 59.99 MB
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Step-by-step instructions, diagrams for creating 35 different polyhedra from origami units — from simple modular cubes to a 14-sided cuboctahedron!

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

Author : Kenneth J. M. MacLean
File Size : 62.86 MB
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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)

A Plethora of Polyhedra in Origami

Author : John Montroll
File Size : 40.74 MB
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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.

Notice on the Symmetrical Polyhedra of Geometry

Author : Auguste Bravais
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Computer Search for Non isomorphic Convex Polyhedra

Author : Donald W. Grace
File Size : 79.29 MB
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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.

On the Minkowski Constant Kantenkruemmung for Special Convex Polyhedra

Author : William James Perry
File Size : 38.21 MB
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Convex Polyhedra with Regular Faces

Author : Viktor A. Zalgaller
File Size : 75.62 MB
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Polyhedra Primer

Author : Peter Pearce
File Size : 83.6 MB
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Here is a lucid, thoughtful guide to understanding the structure and organization of three-dimensional space. In 250 captioned drawings this book communicates the beauty and geometry of polyhedra. Beginning with polygons and tessellations, it proceeds in a logical sequence to finite polyhedra, dual polyhedra, space filling, and open packings. Important considerations of symmetry, periodic and uniform patterns, and regular and semi-regular forms are presented. Because the understanding of polyhedra is enhanced by the manipulation of models, a chapter of both two- and three-dimensional constructions is included.

Three Dimensional Nets and Polyhedra

Author : Alexander Frank Wells
File Size : 83.36 MB
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Convex Figures and Polyhedra

Author : Lazarʹ Aronovich Li︠u︡sternik
File Size : 89.80 MB
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