## Connections: The Geometric Bridge Between Art and ScienceThe first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in “Mathematics, Chemistry, and Astronomy — Professional and Reference” in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. |

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### Contents

Proportion in Architecture | 1 |

Similarity | 35 |

The Golden Mean | 75 |

Graphs | 105 |

Tilings with Polygons | 167 |

TwoDimensional Networks and Lattices | 209 |

Platonic Solids | 255 |

Transformation of the Platonic Solids I | 295 |

Transformation of the Platonic Solids II | 327 |

Space Filling | 347 |

Isometries and Mirrors | 383 |

Symmetry of the Plane | 405 |

Epilogue | 453 |

Supplements | 473 |

487 | |

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### Common terms and phrases

archimedean solids architecture bracing called cells circle color compass and straightedge congruent connected constructed corresponding created crystal cube cuboctahedron curve defined diagonal diagram dodecahedron domains dual edges elements enantiomorphic Equation example faces floor plan fold four fundamental geometric glide reflection golden mean graph grid hexagons icosahedron identical integers intersecting isometries isomorphic Koch snowflake Lalvani lattice length line segments Loeb M. C. Escher mathematics mirror lines Modulor pair parallel pattern Penrose tilings pentagon perpendicular planar planar graph platonic polyhedra platonic solids polyhedron Problem projection properties proportion ratio rectangle regular maps regular tilings result rhombic right triangle rigid rotation rotocenters scale Section self-similar semiregular shown in Figure shows sides similar space space-filling sphere spiral square star star polygons structure surface surrounding symmetry tetrahedron Theorem three-dimensional tion torus transformation translation triangular truncated octahedron vectors vertex figure vertices zonogons zonohedra