tessellation - A collection of shapes that fit together to cover a surface without overlapping or leaving gaps. Often a repeating geometric pattern, many of which may also be referred to as tiling. Types of tessellations include translation, rotation, and reflection. They can be regular or irregular (a regular tessellation is made up of congruent regular polygons — triangles, squares or hexagons), periodic and non-periodic, two- and three-dimensional, and their motifs can be fractals (self-replicating).

Tesselations can be seen in almost every brick wall, tiled floor or wall, quilt pattern, lace tablecloth, fabric and wallpaper pattern.

The study of tessellations can integrate many disciplines across any full curriculum — in art, math, language arts, social studies, etc.

The word "tessellation" comes from the Latin word tessella — the tessera, or small square tile used in producing mosaics.

Examples of tessellations:

United States, Pennsylvania, Quilt, c. 1870-80, Log Cabin pattern, Pineapple variation, wool and cotton, 88 x 88 inches (223.5 x 223.5 cm), Los Angeles County Museum of Art.

Maurits Cornelis Escher (Dutch , 1898-1972), Aarde (Earth), no. 1 from the series De vier elementen (The Four Elements), New Year's greeting card for 1953, 1952, color woodcut printed in blue-gray and brown with letterpress printed in gray; image 15.5 x 13.5 cm; Fine Arts Museums of San Francisco, CA.

Maurits Cornelis Escher, Lucht (Air), no. 2 from the series De vier elementen (The Four Elements), New Year's greeting card for 1954, 1952, color woodcut printed in green and brown with letterpress printed in gray; image 15.4 x 13.4 cm; Fine Arts Museums of San Francisco, CA.

Maurits Cornelis Escher, Vuur (Fire), no. 3 from the series De vier elementen (The Four Elements), New Year's greeting card for 1955, 1952, color woodcut printed in green and brown with letterpress printed in gray; image 15.6 x 13.5 cm; Fine Arts Museums of San Francisco, CA.

Maurits Cornelis Escher, Water, no. 4 from the series De vier elementen (The Four Elements), New Year's greeting card for 1956, 1952, color woodcut printed in green and brown with letterpress printed in gray; image 15.5 x 13.5 cm; Fine Arts Museums of San Francisco, CA.

Maurits Cornelis Escher, Untitled (Reducing Lizards Tessellation).

The scheme Escher devised in producing this tesselation. See gradation.

Marian Bantjes (Canadian, contemporary), Struggle, 2004, digital composite, collection of the artist. If you visit Ms Bantjes' site, be sure to peruse her other patterns and paintings.

• Yahoo's list of tesselation sites.
  
  
• Escher sites:
  • The official M.C. Escher Web site's biography of Escher points out that in addition to impossible figures, he designed postage stamps and tapestries, illustrated books and sometimes worked in three dimensions, carving wooden spheres. The best thing here is a 3-D multimedia section that flies a viewer around and through three of Escher's most famous works. It was developed for a 1998 exhibition in the Netherlands, where, the site says, visitors stood for two hours to watch what can now be seen online: a vivid unraveling of how Escher fooled the eye by compressing multiple viewpoints into one.
  • The World of Escher is a Texas company founded in 1993. It has a gallery, a bibliography and a few Escher quotations, and essays by and about him. It sells a lot of Escher stuff too.
    
    
• Hop's Tessellations is a collection of works, many done in Escher's style by a person named Hop.
  
  
• Totally Tessellated won a ThinkQuest Internet Challenge contest sponsored by a company called Advanced Network and Services, which invites students and their academic coaches to form teams to design educational Web sites.
  
  
• Tessellation lesson plan for 7th grade students.
  
  
• Tantalizing Tessellations. Ten lesson plans aimed at 5th grade (age 11).

Also see Celtic art, fractal, kaleidoscope, metamorphosis, optical illusion, origami, pique assiette (also called picassiette), rhythm, sphere, and textile.

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