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Polyhedra. --- Polyhedra --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Géométrie --- Polytopes --- Geometry --- Géometrie --- Geometry. --- Geometrie --- Polyedres

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Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

Polyhedra --- Polyèdres --- Models --- Data processing --- Modèles --- Geometrical models --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Data processing. --- Models.

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The publication of the first edition of Lagerungen in der Ebene, auf der Kugel und im Raum in 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László Fejes Tóth in his Notes to the 2nd edition. The present version of Lagerungen makes this classic monograph available in English for the first time, with updated Notes, completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original Lagerungen, the revised and updated Notes on the original text, eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come.

Mathematics. --- Math --- Science --- Convex surfaces. --- Polyhedra. --- Sphere. --- Geometry, Solid --- Shapes --- Orbs --- Polyhedral figures --- Polyhedrons --- Convex areas --- Convex domains --- Surfaces --- Superfícies convexes --- Poliedres --- Esfera

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Spaces of constant curvature --- 514.74 --- Algebraic and analytic methods in geometry --- Polyhedra. --- Spaces of constant curvature. --- 514.74 Algebraic and analytic methods in geometry --- Polyhedra --- Constant curvature, Spaces of --- Curvature --- Geometry, Differential --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes

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Molecules, galaxies, art galleries, sculptures, viruses, crystals, architecture, and more: Shaping Space—Exploring Polyhedra in Nature, Art, and the Geometrical Imagination is an exuberant survey of polyhedra and at the same time a hands-on, mind-boggling introduction to one of the oldest and most fascinating branches of mathematics. Some of the world’s leading geometers present a treasury of ideas, history, and culture to make the beauty of polyhedra accessible to students, teachers, polyhedra hobbyists, and professionals such as architects and designers, painters and sculptors, biologists and chemists, crystallographers, physicists and earth scientists, engineers and model builders, mathematicians and computer scientists. The creative chapters by more than 25 authors explore almost every imaginable side of polyhedra.  From the beauty of natural forms to the monumental constructions made by man, there is something to fascinate every reader. The book is dedicated to the memory of the legendary geometer H. S. M. Coxeter and the multifaceted design scientist Arthur L. Loeb. Contributing Authors: P. Ash, T. F. Banchoff, J. Baracs, E. Bolker, C. Chieh, R. Connelly, H.S.M. Coxeter, H. Crapo, E. Demaine, M. Demaine, G. Fleck, B. Grünbaum, I. Hargittai, M. Hargittai, G. Hart, V. Hart, A. Loeb, J. Malkevitch, B. Monson, J. O'Rourke, J. Pedersen, D. Schattschneider, M. Schmitt, E. Schulte, M. Senechal, G.C. Shephard, I. Streinu, M. Walter, M. Wenninger, W. Whiteley, J. M. Wills, and G. M. Ziegler.

Polyhedra. --- Shapes. --- Forms (Shapes) --- Shape --- Polyhedral figures --- Polyhedrons --- Mathematics. --- Design. --- Geometry. --- Crystallography. --- Design, general. --- Geometry --- Surfaces --- Geometry, Solid --- Shapes --- Design and construction. --- Crystallography and Scattering Methods. --- Leptology --- Physical sciences --- Mineralogy --- Mathematics --- Euclid's Elements --- Creation (Literary, artistic, etc.)