Difference between revisions of "Tessellation"

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A '''Tessellation''' is a regular tiling of the infinite plane by [[polygon]]s, or of an infinite three dimensional space by [[polyhedra]], or of an infinite n-dimensional space by [[polytopes]].
 
A '''Tessellation''' is a regular tiling of the infinite plane by [[polygon]]s, or of an infinite three dimensional space by [[polyhedra]], or of an infinite n-dimensional space by [[polytopes]].
  
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[[Image:SemiregularTessellation.gif|right|200px|thumb| The eight semiregular tessellations]]
  
 
===Plane Tessellations===
 
===Plane Tessellations===
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'''Demiregular Tessellations''' are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is different for some of the vertices in the plane. Although it can be argued that the number of such tessellations is infinite, they can be reduced to 14 specific types.
 
'''Demiregular Tessellations''' are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is different for some of the vertices in the plane. Although it can be argued that the number of such tessellations is infinite, they can be reduced to 14 specific types.
 
  
 
===Links===
 
===Links===
  
 
http://mathworld.wolfram.com/Tessellation.html
 
http://mathworld.wolfram.com/Tessellation.html

Revision as of 18:09, 14 May 2007

A Tessellation is a regular tiling of the infinite plane by polygons, or of an infinite three dimensional space by polyhedra, or of an infinite n-dimensional space by polytopes.


The eight semiregular tessellations

Plane Tessellations

Tessellations of the plane can be classified as follows:

Regular Tesselations are comprised of simple repetitions of the same regular polygon. There are three distinct regular tessellations: equilateral triangles, squares and hexagons.


Semiregular Tessellations are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is the same for all vertices in the plane. There are eight such semiregular tessellations.


Demiregular Tessellations are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is different for some of the vertices in the plane. Although it can be argued that the number of such tessellations is infinite, they can be reduced to 14 specific types.

Links

http://mathworld.wolfram.com/Tessellation.html