Symmetries, Patterns and Tessellations

Constructed with Geometer's Sketchpad by Allan Bergmann Jensen.
http://www.geometer.dk/tess/

Artlandia SymmetryWorks

Adobe Illustrator plug-in that automates creation of surface designs and ornaments based on seventeen wallpaper groups. On-line purchase.
http://www.artlandia.com/SymmetryWorks

The Geometry Junkyard: Tilings

A collection of links.
http://www.ics.uci.edu/~eppstein/junkyard/tiling.html

Tessellation Links

Compiled by Suzanne Alejandre for the Math Forum.
http://mathforum.org/sum95/suzanne/links.html

Totally Tessellated

An introduction to tessellations explaining the basic underlying mathematics, and with many examples from real life.
http://library.thinkquest.org/16661/

The Penrose Tiling at Miami University

A summary of the history behind the Penrose tiling in the math department at Miami university.
http://www.lib.muohio.edu/epub/tilings/doc.html

The 14 Different Types of Convex Pentagons that Tile the Plane

Graphics and references.
http://www.mathpuzzle.com/tilepent.html

Grotesque Geometry

Andrew Crompton's tiling and tessellation images.
http://www.cromp.com/tess/home.html

Hop's Escher Tessellation Tiles

Escher-like tessellations.
http://www.tabletoptelephone.com/~hopspage/HopsTiles.html

Hyperbolic Tessellations

Explanations and graphics.
http://aleph0.clarku.edu/~djoyce/poincare/poincare.html

Tessellations with Java

Examples and source code.
http://dimacs.rutgers.edu/~rkrane/tessell.html

Tessellations: Technology and Culture

Examples and Java applets.
http://www.geocities.com/williamwchow/javagraf/javagraf.htm

The Seventeen Wallpaper Groups

Examples in traditional Japanese patterns.
http://mathmuse.sci.ibaraki.ac.jp/pattrn/PatternE.html

Investigating Patterns: Symmetry and Tessellations

Links to activities and other resources.
http://www.camosun.bc.ca/~jbritton/jbsymteslk.htm

Tessellating Wallpaper Patterns

Original tessellating desktop wallpaper tiles.
http://www.geocities.com/hbafscl/tess1.html

Intriguing Tessellations

By Marjorie Rice. Pentagons that tile the plane: details and links.
http://members.aol.com/tessellations/

Tiling Plain and Fancy

Tiling from the mathematical and historical viewpoint by Steve Edwards. Provides a number of examples of various types of tiles that tile the plane and includes periodic tiling plus Penrose's aperiodic tiles.
http://www2.spsu.edu/math/tile/

Tessellations

A company selling foam puzzles, many based on planar tessellations (tilings) and fractals.
http://www.tessellations.com/

Chaos Tiles

This chaotic tiling consists of two equilateral pentagons, with angles (80, 160, 60, 140, 100) and (40, 200, 60, 100, 140). Sets are for sale.
http://www.mathpuzzle.com/chaotile.html

Tessellations Using Geometer's Sketchpad

Description of a class project.
http://www.mste.uiuc.edu/courses/ci336kt/garrison/skpdindx.html

Discrete Plane Symmetry Groups

Web text by Ana Kozomara.
http://www.mi.sanu.ac.yu/vismath/ana/

Symmetry and Pattern: The Art of Oriental Carpets

Resources compiled by the Math Forum.
http://mathforum.org/geometry/rugs/

Alex Bateman's Origami

Tessellation images and software.
http://www.sanger.ac.uk/Users/agb/Origami/origami.html

Escher Patterns

Compiled by Yoshiaki Araki.
http://www.sfc.keio.ac.jp/~aly/escher/

Gallery of Symmetric Chaos

Includes: Symmetric icons and fractals; Quilts and planar repeating patterns; Colored wallpaper patterns.
http://nothung.math.uh.edu/~mike/ag/art.html

Mike Field

University of Houston. Graphics and resources in symmetry and tiling.
http://nothung.math.uh.edu/~mike/

Quasi-Periodic Tilings

Artist Eleni Mylonas uses tilings.
http://www.elenimylonas.com/

Java Penrose Tiler

A Java applet for experimenting with kites and darts.
http://www.geocities.com/SiliconValley/Pines/1684/Penrose.html

Samantha's Wallpaper Page

Wallpaper patterns and symmetry groups.
http://www.geocities.com/hbafscl/

Catalogue of Isohedral Tilings

From the article "One Corona is Enough for the Euclidean Plane" by Doris Schattschneider and Nikolai Dolbilin.
http://mathforum.org/dynamic/one-corona/

Symmetry and the Shape of Space

Chaim Goodman-Strauss, Arkansas. With interactive demos using Geometer's Sketchpad (requires Macintosh).
http://comp.uark.edu/~cgstraus/

Symmetry and the Shape of Space

With interactive demos using Geometer's Sketchpad (requires Macintosh).
http://comp.uark.edu/~cgstraus/symmetry.unit/

Tessellated, Interlocking Concrete Pavers and Molds

Pictures of some concrete tilings.
http://www.geckostone.com/pavers.html

Tilings and Geometric Ornament

Applying principles of computer graphics to the creation of geometric ornament, as a continuation of the tradition of ornamental design using modern tools and algorithms.
http://www.cs.washington.edu/homes/csk/tile/

17 Wall Paper Symmetry Groups to Create a Regular Division of the Plane

Graphics.
http://web.inter.nl.net/hcc/Hans.Kuiper/17system.htm

Hans Kuiper

Hans Kuiper's work. Tessellations and optical art. Also tessellation software with the 17 wallpaper groups.
http://web.inter.nl.net/hcc/Hans.Kuiper/

Tessellation Tutorials by Suzanne Alejandre

Tutorials and templates for making tessellations using ClarisWorks, the Geometer's Sketchpad, HyperCard, HyperStudio, and straightedge and compass, including step-by-step instructions for classroom activities.
http://mathforum.org/sum95/suzanne/tess.intro.html

Penrose Tiles

Links in the Geometry Junkyard.
http://www.ics.uci.edu/~eppstein/junkyard/penrose.html

Pentagons that Tile the Plane

Known solutions and a new recipe.
http://burtleburtle.net/bob/tile/pentagon.html

William's Geometric Construction Page

Activities to create patterns using simple resources, such as making equilateral triangle from a circle. Suitable for upper primary and lower secondary ages.
http://www.cyffredin.co.uk/

Tessellation and Photography

A study for the endless possibilities of tessellating the plane based on the work of Dutch graphic artist M.C. Escher.
http://members.home.nl/wouternimmo

Landry Art

Art of Kenneth Landry. Tessellations, polyhedra and polyhedra decorated with tessellations.
http://www.landryart.com/

Frieze Patterns

Definitions and images.
http://plato.acadiau.ca/courses/educ/reid/Geometry/Symmetry/frieze.html

References about Tessellations

Compiled by Doris Schattschneider, Moravian College.
http://www.geom.uiuc.edu/software/tilings/TilingBibliography.html

KaleidoTile

Software for Macintosh and SGI to create and manipulate tessellations of the sphere, Euclidean plane and hyperbolic plane, and to see how the Platonic solids are related to tessellations.
http://www.geom.uiuc.edu/software/download/KaleidoTile.html

Java Kali

A program for drawing symmetrical patterns based on any of the 17 wallpaper groups, as well as several frieze and rosette groups.
http://www.geom.uiuc.edu/java/Kali/

Wallpaper Groups

Images and descriptions of the 17 plane symmetry groups.
http://www.clarku.edu/~djoyce/wallpaper/

Squared Squares and Squared Rectangles

Tilings of Squared Squares and Squared Rectangles, constructed using javascript.
http://www.squaring.net

Escher Web Sketch

Java applet drawing repeated patterns with selected symmetry.
http://marie.epfl.ch/escher/

TESS

Tessellation software. 11 rosette, all 7 frieze and all 17 wallpaper groups included.
http://www.peda.com/tess/

Investigating Patterns: Symmetry and Tessellations

Links to activities and other resources.
http://britton.disted.camosun.bc.ca/jbsymteslk.htm