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Student Support Services
Tessellations and Art Student Support Services

What is a Tessellation? It is a tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps

Types of Tessellations
Regular Tessellations Semi-regular Tessellations

Regular Tessellations
RULE #1:   The tessellation must tile a floor (that goes on forever) with no overlapping or gaps. RULE #2:  The tiles must be regular polygons - and all the same. RULE #3:   Each vertex must look the same. There are only 2 polygons that will work for regular Tessellations and those are equilateral triangle, hexagon, and a square.

Semi-regular Tessellation
They are made using two or more different regular polygons.

Tessellations and Math
Tessellations use symmetry in Math. Symmetry means that at least one pattern is unchanged. There are four types of Symmetry in the plane.

Types of symmetry in Math
Rotations Translations Reflections Glide reflections

Rotation To rotate an object means to turn it around a point at a certain angle. This point is called the center of rotation.

Translation To translate an object means to move it without rotating or reflecting it. Every translation has a direction and a distance.

Reflection To reflect an object means to produce its mirror image. Every reflection has a mirror line. A reflection of an "R" is a backwards "R".

Glide Reflection A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involve more than one step.

A few uses of symmetry Patterns for shoe bottoms. Parking lot design.
Design color pattern for neckties and t-shirts. Design wallpaper for interior decoration

How is Tessellations used in Art?
First, the artist will cut out a shape and then will decide what this particular shape looks like. For example, what does this look like?

Tessellations and Art Then the artist tessellated it.

Tessellations and Art He thought it looked like a house so he colored it in like this:

Tessellations and Art Here is another example. What does this look like?

Tessellations and Art This is what the artist saw and how he tessellated it.

Tessellations and Art You can also take a shape, tessellate it and then color it in, like this:

Tessellations and Art Now it is your turn! We are going to be doing one like the previous one we just saw. Have fun!