Title: Tessellations
1Tessellations
Lesson 10-4
2A tessellation is a design or pattern in which a
shape is use repeatedly to cover a plane with no
gaps, overlaps, or empty spaces.
Tessellations
- 1. A regular tessellation is a pattern made with
only one type of regular polygon. - 2. The sum of the measures surrounding a point
(or vertex) must be 360. - 3. Only regular polygons that have an interior
angle which is a factor of 360 will tessellate. - 4. No regular polygon with more than 6 sides can
be used in a regular tessellation.
3Can these figures form a regular tessellation?
No. Although this is a regular polygon, it has
an interior angle 135, which is not a factor
of 360
Yes. This is a regular polygon with a 90
interior angle which is a factor of 360.
Yes. This is a regular polygon with a 120
interior angle, which is a factor of 360.
4Can these figures form a regular tessellation?
Yes. This is a regular polygon with a 60
interior angle which is a factor of 360.
No. This is not a regular polygon. It can
tessellate but not in a regular tessellation.
No. This is not a regular polygon. It can
tessellate but not in a regular tessellation.
5How about these for regular tessellation?
- 1. a 20-sided figure?
- No, because its interior angle is 162, which is
not a factor of 360. - (Interior angle measure 180(20 - 2) 162
-
20 - 2. a 10-sided figure?
- No, the interior angle is 144 (not a factor of
360). - 3. a 12-sided figure?
- No, the interior angle is 150 (not a factor of
360). - Note No regular polygon with more than six
sides can be used in a regular tessellation.
6Semi-regular Tessellations
- If the same combination of regular polygons meet
at each vertex, it is called a semi-regular
tessellation.
Notice the regular octagons with interior angles
of 135 and the squares with 90. At each vertex
or point, there is a sum of 135 135 90 360.
7Irregular Tessellations
- Other figures can make tessellations which are
irregular. The figures used are irregular
polygons and may be the same or different types.
- Here is an irregular tessellation made with kites
and one with trapezoids.
8Make a special tessellation!
- 1. Begin with a rectangle.
- 2. Cut a piece out of it and stick on another
side. - 3. Translate the new figure to create a
tessellation.
9Or another . . .
- Start with a triangle
- 2. Cut out a piece of it and slide it to another
side. - Slide and reflect the figure repeatedly
- to create a tessellation.
10Special Notes on Tessellations
- 1. At each vertex of a tessellation, the sum of
the measures of the angles must equal 360. - 2. Any quadrilateral will tessellate.
- 3. Combinations of figures can be used to
tessellate. - 4. Only equilateral triangles, squares, and
regular hexagons can make regular tessellations.