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Tessellations

Science > Math > Recreations > Tessellations

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17 Wall Paper Symmetry Groups to Create a Regular Division of the Plane - http://web.inter.nl.net/hcc/Hans.Kuiper/17system.htm
Graphics.

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

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

Chaos Tiles - http://www.mathpuzzle.com/chaotile.html
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.

Escher Patterns - http://britton.disted.camosun.bc.ca/jbaraki.htm
Compiled by Yoshiaki Araki.

Escher Web Sketch - http://escher.epfl.ch/escher/
Java applet drawing repeated patterns with selected symmetry.

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

Gallery of Symmetric Chaos - http://www.math.uh.edu/~mike/ag/art.html
Includes symmetric icons and fractals, quilts and planar repeating patterns and colored wallpaper patterns.

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

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

Hop's Escher Tessellation Tiles - http://www.tabletoptelephone.com/~hopspage/HopsTiles.html
Escher-like tessellations.

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

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

Intriguing Tessellations - http://tessellations.home.comcast.net/~tessellations/
By Marjorie Rice. Pentagons that tile the plane. Includes details and links.

Investigating Patterns: Symmetry and Tessellations - http://britton.disted.camosun.bc.ca/jbsymteslk.htm
Links to activities and other resources.

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

KaleidoTile - http://www.geom.uiuc.edu/software/download/KaleidoTile.html
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.

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

Mike Field - http://www.math.uh.edu/~mike/
University of Houston. Graphics and resources in symmetry and tiling.

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

Pentagons that Tile the Plane - http://burtleburtle.net/bob/tile/pentagon.html
Known solutions and a new recipe.

Quasi-Periodic Tilings - http://www.elenimylonas.com/
Artist Eleni Mylonas uses tilings.

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

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

Symmetry and Pattern: The Art of Oriental Carpets - http://mathforum.org/geometry/rugs/
Resources compiled by the Math Forum.

Symmetry and the Shape of Space - http://comp.uark.edu/~strauss/symmetry.unit/
With interactive demos using Geometer's Sketchpad (requires Macintosh).

Tessellated, Interlocking Concrete Pavers and Molds - http://www.geckostone.com/pavers.html
Pictures of some concrete tilings.

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

Tessellation Tutorials by Suzanne Alejandre - http://mathforum.org/sum95/suzanne/tess.intro.html
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.

Tessellations - http://members.cox.net/tessellations/
A company selling foam puzzles, many based on planar tessellations (tilings) and fractals.

Tessellations with Java - http://dimacs.rutgers.edu/~rkrane/tessell.html
Examples and source code.

The 14 Different Types of Convex Pentagons that Tile the Plane - http://www.mathpuzzle.com/tilepent.html
Graphics and references.

The Geometry Junkyard: Tilings - http://www.ics.uci.edu/~eppstein/junkyard/tiling.html
A collection of links.

The Seventeen Wallpaper Groups - http://mathmuse.sci.ibaraki.ac.jp/pattrn/PatternE.html
Examples in traditional Japanese patterns.

Tiling Plain and Fancy - http://www2.spsu.edu/math/tile/
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.

Tilings and Geometric Ornament - http://www.cgl.uwaterloo.ca/~csk/washington/tile/
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.

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

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

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

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