TESSELLATIONSTESSELLATIONSTESSELLATIONSTESSELLATIONS

DefinitionDefinition A tessellation is a tiling

of a plane with a shape or shapes without creating any gaps or overlaps

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

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

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

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)

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

EscherEscher M.C. Escher, the Dutch

artist, is famous for his many pictures of periodic tilings with shapes that resemble living things

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

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

TessellationsTessellations PeriodicPeriodic

– RegularRegular– SemiregularSemiregular– Not SemiregularNot Semiregular– IrregularIrregular

AperiodicAperiodic

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

For more information seehttp://www.ScienceU.com/geometry/articles/tiling/http://library.thinkquest.org/