JENIS2 TESELASI

8/14/2019 JENIS2 TESELASI

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Tessellations

Tessellation Definition

A tessellation is created when a shape isrepeated over and over again covering a

plane without any gaps or overlaps.

Another word for a tessellation is a tiling .

Tiling Definition

When you fit individual tiles together withno gaps or overlaps to fill a flat space like aceiling, wall, or floor, you have a tiling.


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What areTessellations

The word'tessera' in latinmeans a smallstone cube.They were usedto make up'tessellata' - themosaic picturesforming floorsand tilings inoman

buildingsThe term has

become morespecialised andis often used torefer to picturesor tiles, mostlyin the form ofanimals andother lifeforms, whichcover thesurface of a

plane in asymmetricalway withoutoverlapping orleaving gaps.


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Symmetry

!f you look at a completedtessellation, you will see the originalmotif repeats in a pattern. "nemathematical idea that can beemphasi#ed through tessellations issymmetry.

There are $% possible ways that a pattern can be used to tile a flatsurface or 'wallpaper'.

&olya $%

ways to tilea surface

(scher read &)lya's $*+ paperon plane symmetry groups.(scherunderstood the $% planesymmetry groups described in themathematician &)lya's paper,even though he didn't understandthe abstract concept of the groupsdiscussed in the paper.

etween $* / and $* + (scher produced colored drawingswith a wide variety of symmetrytypes while working on possible

periodic tilings. 0e adopted ahighly mathematical approachwith a systematic study using anotation which he inventedhimself.


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Four Types of Symmetry in aPlane

There are ways of moving a motif to

another position in the pattern. Thesewere described by (scher.

Translation eflection otation

1lide eflection

Translation eflection otation 1lide eflection

A translationis a shape thatis simplytranslated, orslid, acrossthe paper anddrawn againin another

place.

Thetranslationshows thegeometricshape in thesamealignment asthe original2 itdoes not turnor flip.

A reflection is ashape that has

been flipped.3ost commonlyflipped directly tothe left or right4over a 5y5 a6is7 orflipped to the topor bottom 4over an565 a6is7,reflections canalso be done at anangle.

!f a reflection has been donecorrectly, you candraw an imaginaryline right throughthe middle, and thetwo parts will besymmetrical5mirror5 images.To reflect a shapeacross an a6is is to

plot a special

otation is spinning the pattern around a point,rotating it. A rotation, orturn, occurs when anob8ect is moved in acircular fashion around acentral point which doesnot move.

A good e6ample of arotation is one 5wing5 ofa pinwheel which turnsaround the center

point. otations alwayshave a center, and anangle of rotation.

!n glide reflection, reflectionand translation are usedconcurrently much like thefollowing piece by (scher,0orseman. There is noreflectional symmetry, nor isthere rotational symmetry.


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corresponding point for every point in theoriginal shape.

&entomino 9hapes

A pentomino is the shape of five connected checkerboards:uares. There are only twelve different pentomino shapes

Rectangles


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Triangles

Hexagons

(scher painted this study of a tile fromthe Alhambra.


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(scher works based on a circle


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Tesselation to thelimit of a circle.

IslamicTil

es

Theseare star

patterntiles.


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0ere

aremore!slamic star

patter n tiles.


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Tessellationswith a3-Deffect

sch


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scher

sch


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