Creating a Translation Tessellation

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How do you create different types of
tessellations?
Tessellation done by David Anal on
tessellation.org
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What is a TESSELLATION?

• A tessellation is a tiled pattern formed by
  repeating figures to fill a plane without gaps or
  overlaps.
• You can use geometric transformations to create
  tessellations
• Three types of transformations are translation,
  reflection, rotation.

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Translation

• You slide a figure from one position to another.

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Reflection

• The flip of a figure over a line to produce a
  mirror image.

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Rotation

• A geometric turn of a figure around a fixed
  point.

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Creating a Translation Tessellation
Tessellation done by David Anal on
tessellation.org
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1. Cut out a shape from vertex to vertex on one
side.
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2. Translate the cut out to the opposite side and
attach.
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3. Repeat steps 1 and 2 with remaining opposite
sides
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The finished product!
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Watch it tessellate!
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Creating a Rotation Tessellation
Tessellation done by David Anal from
tessellation.org
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1. Cut out a shape from vertex to vertex on one
side.
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Pick an endpoint as the center of rotation

• Rotate the cut-out to the adjacent
• side (90 degrees clockwise or
  counterclockwise)

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3. Repeat steps 1 and 2 with the other two
adjacent sides
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3. Repeat steps 1 and 2 with the other two
adjacent sides
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The finished product
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Watch it tessellate!
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Creating a Glide-Reflection Tessellation.
Tessellation done by David Anal on
tessellation.org
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1. Cut out a shape from one side.
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2. Glide the shape to the opposite side.
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3. Cut out a shape from one of the remaining
sides and glide it to the opposite side. DO NOT
ATTACH!
Not taped!
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4. Now reflect that final glide.
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The finished product.
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Watch it tessellate!
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Are tessellations useful?

• http//www.netropolitan.org/moss/beehive.html
• http//www.toytrux.com/pins/199820_Hess_Soccer_Ba
  ll.JPG
• http//classes.uleth.ca/200301/fa2020a/Images/CRAC
  KERS.JPG

Here are some sites that have examples of
tessellations used in the real-world.
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http//classes.uleth.ca/200301/fa2020a/Images/CRAC
KERS.JPG
Resources
Key Curriculum Technologies (2001). The
Geometers Sketchpad (version 4.06)
computer software
Serra, M.(1993). Discovering geometry an
inductive Approach. Key Curriculum.
Websites for pictures

• http//www.tessellations.org/index.htm

http//www.netropolitan.org/moss/beehive.html
http//www.toytrux.com/pins/199820_Hess_Soccer_Ba
ll.JPG