Origami Polyhedra Design PDF
Preview Origami Polyhedra Design
Origami Polyhedra Design Origami Polyhedra Design John Montroll A K Peters, Ltd. Natick, Massachusetts CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150225 International Standard Book Number-13: 978-1-4398-7106-5 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To Himanshu Contents Symbols xi Basic Folds xii Introduction xiii Part I: Designing Origami Polyhedra 1 Polyhedra Overview 3 Design Factors and Techniques 7 Math and Design 19 Design Method Examples 39 Polygons 45 Equilateral Triangle ✩ 46 Pentagon ✩ 48 Hexagon ✩ 52 Heptagon ✩ 54 Octagon ✩ 56 Silver Rectangle ✩ 57 Bronze Rectangle ✩ 58 Golden Rectangle ✩ 59 Part II: Platonic and Related Polyhedra 61 Tetrahedron Design 63 Tetrahedron ✩ 65 Duo-Colored Tetrahedron ✩✩ 67 Striped Tetrahedron ✩✩ 69 Tetrahedron of Triangles ✩✩ 72 Stellated Tetrahedron ✩✩ 76 Dimpled Truncated Tetrahedron ✩✩✩ 79 Cube Design 83 Cube ✩✩ 87 Striped Cube ✩✩ 89 Triangles on Cube ✩✩ 92 Cube with Squares ✩✩ 95 Stellated Octahedron ✩✩ 98 Cubehemioctahedron ✩✩✩ 100 Dimpled Rhombicuboctahedron ✩✩✩ 104 Stacked Cubes ✩✩✩✩ 108 Simple ✩ Intermediate ✩✩ Complex ✩✩✩ Very Complex ✩✩✩✩ Octahedron Design 113 Octahedron ✩✩ 115 Striped Octahedron ✩✩ 118 Duo-Colored Octahedron ✩✩ 121 Stellated Cube ✩✩ 124 Octahemioctahedron ✩✩✩ 127 Dimpled Truncated Octahedron ✩✩✩ 131 More Platonic Solids Design 135 Icosahedron ✩✩✩ 137 Dodecahedron ✩✩✩✩ 140 Sunken Platonic Solids Design 147 Sunken Octahedron ✩✩ 150 Sunken Tetrahedron ✩✩✩ 153 Sunken Cube ✩✩✩ 157 Sunken Dodecahedron ✩✩✩✩ 161 Sunken Icosahedron ✩✩✩✩ 166 Part III: Dipyramids and Dimpled Dipyramids 171 Dipyramid Design 173 Triangular Dipyramid 90° ✩ 178 Triangular Dipyramid ✩✩ 180 Triangular Dipyramid in a Sphere ✩✩ 183 Tall Triangular Dipyramid ✩✩ 186 Tall Square Dipyramid ✩✩ 189 Silver Square Dipyramid ✩✩ 192 Squat Silver Square Diamond ✩✩ 194 Pentagonal Dipyramid ✩✩ 197 Pentagonal Dipyramid 45° ✩✩ 201 Pentagonal Dipyramid in a Sphere ✩✩ 203 Golden Pentagonal Dipyramid ✩✩ 206 Squat Golden Pentagonal Dipyramid ✩✩ 208 Hexagonal Dipyramid ✩✩ 210 Silver Hexagonal Dipyramid ✩✩ 213 Hexagonal Dipyramid 36° ✩✩ 214 Hexagonal Dipyramid in a Sphere ✩✩ 215 Squat Silver Hexagonal Dipyramid ✩✩ 218 Heptagonal Dipyramid ✩✩✩ 219 Heptagonal Dipyramid 30° ✩✩✩ 223 Heptagonal Dipyramid in a Sphere ✩✩✩ 225 Octagonal Dipyramid ✩✩✩ 229 Octagonal Dipyramid 26° ✩✩✩ 232 Octagonal Dipyramid in a Sphere ✩✩✩ 234 Nonagonal Dipyramid ✩✩✩ 237 Decagonal Dipyramid ✩✩✩ 240 viii Contents Dimpled Dipyramid Design 243 Tall Dimpled Square Dipyramid ✩✩ 247 Dimpled Silver Sqare Dipyramid ✩✩✩ 250 Heptahedron ✩✩✩ 254 Dimpled Squat Square Dipyramid ✩✩✩ 258 Tall Dimpled Hexagonal Dipyramid ✩✩✩✩ 262 Dimpled Silver Hexagonal Dipyramid ✩✩✩✩ 267 Dimpled Hexagonal Dypyramid ✩✩✩✩ 270 Dimpled Hexagonal Dipyramid in a Sphere ✩✩✩✩ 275 Octagonal Flying Saucer ✩✩ 280 Dimpled Octagonal Dipyramid in a Sphere ✩✩✩ 283 Dimpled Octagonal Dipyramid ✩✩✩ 287 Dimpled Silver Octagonal Dipyramid ✩✩✩ 288 Contents ix
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