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A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. The tessellation is perhaps most well-known today for its use in the art of M.C. Escher.
In Latin, tessella was a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellation, often made of glazed clay.
Wallpaper groups
More on [ Tessellation ]
Escher, M. C. :: E
Geometry :: Math
Polytopes :: Geometry
doing homework, studying... (NOT)
tessellations (elli hernandez) Thu, 07 Jan 2010 05:21:12 -0000
doing homework, studying... (NOT)
@Atouchofglitter Lmao you are blown!!! Get swoll
tessellations (elli hernandez) Wed, 06 Jan 2010 19:41:30 -0000
@Atouchofglitter Lmao you are blown!!! Get swoll
Say wat?
tessellations (elli hernandez) Wed, 06 Jan 2010 19:38:48 -0000
Say wat?
Blehh! Stauin aft school with seth, later:)
tessellations (elli hernandez) Wed, 06 Jan 2010 18:16:30 -0000
Blehh! Stauin aft school with seth, later:)
If government isn't the worst class ever, then i don't know what is
tessellations (elli hernandez) Wed, 06 Jan 2010 14:17:00 -0000
If government isn't the worst class ever, then i don't know what is
@atouchofglitter lmao whatd you do
tessellations (elli hernandez) Wed, 06 Jan 2010 02:24:17 -0000
@atouchofglitter lmao whatd you do
17 Wall Paper Symmetry Groups to Create a Regular Division of the Plane - Graphics.
Artlandia SymmetryWorks - Adobe Illustrator plug-in that automates creation of surface designs and ornaments based on seventeen wallpaper groups. On-line purchase.
Meta Description: [ Artlandia SymmetryWorks is a powerful software for creating repeat patterns. This Adobe Illustrator plug-in lets you make complex pattern designs in seconds. ]
Catalogue of Isohedral Tilings - From the article One Corona is Enough for the Euclidean Plane by Doris Schattschneider and Nikolai Dolbilin.
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.
Discrete Plane Symmetry Groups - Web text by Ana Kozomara.
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Escher Patterns - Compiled by Yoshiaki Araki.
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Escher Web Sketch - Java applet drawing repeated patterns with selected symmetry.
Frieze Patterns - Definitions and images.
Gallery of Symmetric Chaos - Includes: Symmetric icons and fractals; Quilts and planar repeating patterns; Colored wallpaper patterns.
Meta Description: [ computer graphics, symmetric chaos, patterns, symmetry ]
Grotesque Geometry - Andrew Crompton's tiling and tessellation images.
Hans Kuiper - Hans Kuiper's work. Tessellations and optical art. Also tessellation software with the 17 wallpaper groups.
Hop's Escher Tessellation Tiles - Escher-like tessellations.
Meta Description: [ Escher like tessellations that I made. ]
Hyperbolic Tessellations - Explanations and graphics.
Intriguing Tessellations - By Marjorie Rice. Pentagons that tile the plane: details and links.
Investigating Patterns: Symmetry and Tessellations - Links to activities and other resources.
Meta Description: [ Annotated links to over 150 web sites that illustrate symmetry and tessellations. Organized into 30 learning activities that are correlated to a middle school math text. ]
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 - 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 - Art of Kenneth Landry. Tessellations, polyhedra and polyhedra decorated with tessellations.
Meta Description: [ Seattle artist Kenneth Landry's prints, illustrations, and tessellations ]
Mike Field - University of Houston. Graphics and resources in symmetry and tiling.
Meta Description: [ computer graphics, symmetric chaos, patterns, symmetry ]
Penrose Tiles - Links in the Geometry Junkyard.
Pentagons that Tile the Plane - Known solutions and a new recipe.
Quasi-Periodic Tilings - Artist Eleni Mylonas uses tilings.
Meta Description: [ Welcome to Eleni Mylonas' web site - Artist, Photographer, Sculpturer. ]
References about Tessellations - Compiled by Doris Schattschneider, Moravian College.
Squared Squares and Squared Rectangles - Tilings of Squared Squares and Squared Rectangles, constructed using javascript.
Symmetries, Patterns and Tessellations - Constructed with Geometer's Sketchpad by Allan Bergmann Jensen.
Symmetry and Pattern: The Art of Oriental Carpets - Resources compiled by the Math Forum.
Meta Description: [ In this online exhibit, the study of
symmetry is used to analyze patterns in Oriental carpets. A joint project of
The Textile Museum and The Math Forum. ]
Symmetry and the Shape of Space - Chaim Goodman-Strauss, Arkansas. With interactive demos using Geometer's Sketchpad (requires Macintosh).
Symmetry and the Shape of Space - With interactive demos using Geometer's Sketchpad (requires Macintosh).
TESS - Tessellation software. 11 rosette, all 7 frieze and all 17 wallpaper groups included.
Tessellated, Interlocking Concrete Pavers and Molds - Pictures of some concrete tilings.
Tessellation and Photography - A study for the endless possibilities of tessellating the plane based on the work of Dutch graphic artist M.C. Escher.
Meta Description: [ Escher inspired me to study the endless possibilities of tessellations and soon I started making my own. ]
Tessellation Links - Compiled by Suzanne Alejandre for the Math Forum.
Meta Description: [ Links to other sites about tessellations. ]
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.
Meta Description: [ 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 - A company selling foam puzzles, many based on planar tessellations (tilings) and fractals.
Tessellations Using Geometer's Sketchpad - Description of a class project.
Tessellations with Java - Examples and source code.
The 14 Different Types of Convex Pentagons that Tile the Plane - Graphics and references.
The Geometry Junkyard: Tilings - A collection of links.
The Penrose Tiling at Miami University - A summary of the history behind the Penrose tiling in the math department at Miami university.
The Seventeen Wallpaper Groups - Examples in traditional Japanese patterns.
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.
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.
Totally Tessellated - An introduction to tessellations explaining the basic underlying mathematics, and with many examples from real life.
Wallpaper Groups - Images and descriptions of the 17 plane symmetry groups.
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.
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