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Tessellations

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Lesson 10-4 Tessellations A tessellation is a design or pattern in which a shape is use repeatedly to cover a plane with no gaps, overlaps, or empty spaces. – PowerPoint PPT presentation

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Title: Tessellations


1
Tessellations
Lesson 10-4
2
A 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.

3
Can 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.
4
Can 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.
5
How 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.

6
Semi-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.
7
Irregular 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.

8
Make 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.

9
Or 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.

10
Special 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.
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