TESSELLATIONSTESSELLATIONS. cDefinition c cA tessellation is a tiling of a plane with a shape or...
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Transcript of TESSELLATIONSTESSELLATIONS. cDefinition c cA tessellation is a tiling of a plane with a shape or...
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TESSELLATIONSTESSELLATIONSTESSELLATIONSTESSELLATIONS
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DefinitionDefinition A tessellation is a tiling
of a plane with a shape or shapes without creating any gaps or overlaps
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PeriodicPeriodic A periodic tessellation is
one on which you can outline a region that tiles the plane by translation, that is, by shifting the position of the region without rotating or reflecting
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Periodic: RegularPeriodic: Regular A regular tessellation is a
tiling in which only one shape is used
The shape must have congruent sides and congruent angles
There exists exactly three regular tessellations
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Periodic: SemiregularPeriodic: Semiregular A semi-regular
tessellation is when more than one regular shape is used to tile a plane
Every vertex has the same combination of shapes
There are only eight such tessellations
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Periodic: Not SemiregularPeriodic: Not Semiregular The vertices do not
have the same combination of shapes A
B
A (3.4.6.4)
B (3.3.4.3.4)
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Periodic: IrregularPeriodic: Irregular An irregular tessellation
is one in which nonregular shapes are used
An infinite number of shapes tile periodically
Any quadrilateral will tessellate
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EscherEscher M.C. Escher, the Dutch
artist, is famous for his many pictures of periodic tilings with shapes that resemble living things
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AperiodicAperiodic In an aperiodic
(nonperiodic) tessellation translation alone is not used to cover the plane. Shapes are rotated and reflected as well.
An infinite number of shapes tile only periodically
An infinite number of shapes tile both periodically and aperiodically
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PenrosePenrose Roger Penrose found a
pair of tiles that force aperiodicity. In other words, they can not tile by translation alone.
As the patterns expand, they seem to strive to repeat but as you continue out they are not the same
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TessellationsTessellations PeriodicPeriodic
– RegularRegular– SemiregularSemiregular– Not SemiregularNot Semiregular– IrregularIrregular
AperiodicAperiodic
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CreditsCreditsProduced by Dottie Feinstein © 1997 (2007)
Conti, Shrines of Power, HBJ Press, 1978
Gardner, Penrose Tiles to Trapdoor Ciphers,W.H. Freeman & Co., 1989
Tessellation Poster: Teaching Notes, Dale Seymour, 1987
Produced by Dottie Feinstein © 1997 (2007)
Conti, Shrines of Power, HBJ Press, 1978
Gardner, Penrose Tiles to Trapdoor Ciphers,W.H. Freeman & Co., 1989
Tessellation Poster: Teaching Notes, Dale Seymour, 1987
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For more information seehttp://www.ScienceU.com/geometry/articles/tiling/http://library.thinkquest.org/