Tessellations

1
Tessellations

• Advanced Geometry
• Rigid Transformations
• Lesson 4

2
Symmetry

• Figures that are indistinguishable following a
  transformation have symmetry.

3
Tessellation
pattern
no overlapping or empty spaces
On the left is a true tessellation
on the right is not a tessellation but a pattern.
4
Tessellations repeat and have clearly defined
closed shapes.
Patterns repeat but do not have clearly defined
closed shapes.
5
Regular Tessellation
one type of REGULAR POLYGON


Equilateral triangles
Squares
Regular hexagons
6
Uniform Tessellation
the same arrangement
of shapes and angles at each vertex
7
Semi-regular Tessellation
uniform
two or more regular polygons
8
Example
Determine whether each polygon tessellates the
plane. If so, describe the tessellation as
uniform, not uniform, regular, or semi-regular.
9
We must determine if certain polygons tessellate
the plane.
Look at the angle measures at each vertex to
decide.
The angles at every vertex must have a sum of
EXACTLY 360.
10
Angles of a Regular Polygon
180(n 2)
First find the sum of the angles of the polygon.
n of angles
Sum
Then divide by the number of angles.
n
11
Example Determine whether a regular 16-gon
tessellates the plane. Explain.
12
Example
Determine whether each polygon or set of
polygons tessellates the plane. If so, describe
the tessellation as uniform, not uniform,
regular, or semi-regular.
13
Example Determine whether a semi-regular
tessellation can be created from each set of
figures. Assume that each figure has side
length of 1 unit.
regular pentagon and square
14
Example Determine whether a semi-regular
tessellation can be created from each set of
figures. Assume that each figure has side
length of 1 unit.
squares and equilateral triangles
15
Example Stained glass is a very popular
design selection for church and cathedral
windows. Determine whether the pattern is
a tessellation. If so, describe it as
uniform, not uniform, regular, or semi-regular.