When and how did you get interested in tessellations? I asked Sam a few questions about his work: If this has got you inspired, send me your tessellations and I'll put them up on a post at a later date. "Once your tiles are finished, all that is left to be done is to repeat them into their formation and your tessellation is complete." STAGE FIVE: Assembling your tessellation Photograph: Sam Kerr 138 Other aperiodic sets and substitution tilings. Matching Rules, Aperiodic Tiles, and Substitution Tilings. Rosettes and Spirals.115 Rhombus rosettes. 106 The translation and Conway criteria.108 Other recreations using polyforms.108 Heesch number. 103 Properties of polyforms.104 Tessellations of polyforms. 97 Games and puzzles.98 Islamic art and architecture. 89 Tiling.89 Building blocks and coverings.90 Permeable barriers. Decorative and Utilitarian Tessellations. Modeling natural tessellations using geometric tessellations. Quantitative analysis of natural tessellations. 79 Cracking and crazing.79 Divisions in plants and animals.80 Coloration in animals.83 Voronoi tessellations.83 Activity 4.1. Glide refection symmetry in tessellations. Identifying transformations.72 Activity 3.3. Identifying symmetry in objects.70 Activity 3.2. 65 p6 (632).65 p6m (*632).65 Heesch types and orbifold notation.65 Coloring of tessellations and symmetry. Symmetry and Transformations in Tessellations. Classifying tessellations by their vertices.50 3. Classifying tessellations by their vertices. Basic properties of tiles.45 Worksheet 2.1. 38 Circle packings and tessellations.42 Activity 2.1. 36 Squared squares.37 Modifying tessellations to create new tessellations. 31 Star polygon tessellations.33 Regular polygon tessellations that are not edge-to-edge. 27 Pentagon and hexagon tessellations.29 Stellation of regular polygons and star polygons. 25 Dual tessellations and Laves tessellations. 24 General triangle and quadrilateral tessellations. 20 Regular-polygon vertices.21 Prototiles.23 Semi-regular tessellations.23 Other types of polygons. 19 Regular polygons and regular tessellations. 18 Vertices and edge-to-edge tessellations. 9 Tessellations and mathematics education. 4 Escheresque tessellations.5 Tessellations and recreational mathematics. 1 Historical examples of tessellations.2 Tessellations in the world around us. F384 2020 (print) | LCC QA166.8 (ebook) | DDC 516/.132-dc23 LC record available at LC ebook record available at ISBN: 9780367185961 (pbk) ISBN: 9780367185978 (hbk) ISBN: 9780429197123 (ebk) Typeset in Avenir by Deanta Global Publishing Services, Chennai, India Contents 2. | Includes bibliographical references and index. Description: Boca Raton : AK Peters/CRC Press, 2021. Title: Tessellations : mathematics, art, and recreation / Robert Fathauer. Library of Congress Cataloging-in-Publication Data Names: Fathauer, Robert W., author. For works that are not available on CCC please contact Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identifcation and explanation without intent to infringe. For permission to photocopy or use material electronically from this work, access or contact the Copyright Clearance Center, Inc. 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, microflming, and recording, or in any information storage or retrieval system, without written permission from the publishers. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Te 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. TESSELLATIONS Mathematics, Art, and Recreation Robert Fathauer First edition published 2021 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN © 2021 Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, LLC Reasonable eforts 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.
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