6th Grade Math Textbook, Fundamentals

 &KDSWHU

10-11

Tessellations

Objective To identify polygons that tessellate • To identify translation tessellation and

rotation tessellation • To make figures for translation tessellations and rotation tessellations

Sadiq has been commissioned to create a large mural
for the entrance to a local art museum. He decides to
use tessellations to create this mural.

Before creating the mural, Sadiq knows that he must
first choose a polygon that tessellates. What are some
of the possibilities from which he could choose?

 are the covering of a plane with congruent

copies of the same figure or figures with no overlaps or gaps.

This kind of design has been used in art for centuries.

A is a pattern made by translating

or sliding a figure. Any parallelogram can be used to create

a translation tessellation.

You can also create translation tessellations from more interesting

shapes by following these steps:

Start with any parallelogram, and cut a shape from one side.

Translate (or slide) the cut-out shape to the opposite side

of the parallelogram.

If desired, repeat Steps 1 and 2 with the other pairs of sides.

Fit copies of the figure together.

translation tessellation

Tessellations

Remember:Rhombuses,

rectangles, and squares

are all different types of

parallelograms.

A uses rotated figures to create a pattern.

A regular rotation tessellation uses regular polygons. Only figures

with angles that are factors of 360 can be used to create rotation

tessellations. At the point where vertices meet, the total angle

measure of all the angles must equal 360 to form a tessellation.

So squares, regular hexagons, and equilateral triangles

all tessellate: 90° • 4 360°; 60° • 6 360°; 120° • 3 360°.

rotation tessellation Remember:

A regular polygon has

all congruent sides and

all congruent angles.

Each angle of a square

is 90°.

Each angle of an

equilateral triangle is 60°.

Each angle of a regular

360° hexagon is 120°.

360°

360°

So Sadiq could use parallelograms, equilateral triangles, or regular

hexagons for the mural.