The symmetries of things

Start with a single shape. Repeat it in some way-translation, reflection over a line, rotation around a point-and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. I...

• Main Author: Conway, John Horton 1937-2020
• Other Authors: Burgiel, Heidi, Goodman-Strauss, Chaim
• Format: Book
• Language: English
• Published: Baton Rouge: A K Peters/CRC Press, 2008
• Subjects: Geometry; Geometría; Shapes; Symmetry; Mathematics
• Online Access: Texto completo

Table of Contents:

• Symmetries
• Planar patterns
• The magic theorem
• The spherical patterns
• Frieze patterns
• Why the magic theorems work
• Euler’s map theorem
• Classification of surfaces
• Orbifolds
• Presenting presentations
• Twofold colorations
• Threefold colorings of plane patterns
• Other primefold colorings
• Searching for relations
• Types of tilings
• Abstract groups
• Introducing hyperbolic groups
• More on hyperbolic groups
• Archimedean tilings
• Generalized Schläfli symbols
• Naming archimedean and catalan polyhedra and tilings
• The 35 “Prime” space groups
• Objects with prime symmetry