## M.C. Escher: Visions of SymmetryDoris Schattschneider's Visions of Symmetry is a study of Escher's work. It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzlelike interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by analyzing Escher's notebooks. Visions of Symmetry includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. This new edition also features a foreward and an illustrated epilogue that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists. |

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### Contents

Early signs 2 The fascination of regular division of the plane | 9 |

An important journey 15 The open gate 19 The geometric | 44 |

The 19411942 notebooks 54 Eschers theory in relation | 98 |

Copyright | |

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### Common terms and phrases

200 mm image 230 mm sheet A3 type adjacent motifs artist bank-note background birds block carved color symmetry colored pencil column congruent contrasting color create crystallographers decorative diagonal Drawn at Baarn Drawn at Ukkel edges Escher notes Escher refers Escher system Escher's drawing Escher's periodic drawings Escher's prints example figures fill the plane fish folio four glide-reflection Grafiek en tekeningen H. S. M. Coxeter Hague-GM half-turn centers Heesch hexagons IA-IA IIA-IIIA illustrations India ink intarsia interlocked isohedral lizards M. C. Escher mathematical mathematicians Metamorphosis Metamorphosis III mirror image motifs notebook outline panel parallelograms PERIODIC DESIGN Periodic Drawings plate plane filling Polya's polygons Published in Periodic reflection symmetry Regelmatige vlakverdeling regular division Related graphic rhombus rotation Sachs shape shows single motif sketch square surface Symmetry group pi tessellations theory tiles tion transformations transitional system translation variant vertices visual watercolor Woodcut