What if you were given a hexagon and asked to tile it over a plane such that it would fill the plane with no overlaps and no gaps? Could you do this?
You have probably seen tessellations before, even though you did not call them that. Examples of tessellations are: a tile floor, a brick or block wall, a checker or chess board, and a fabric pattern. A tessellation is a tiling over a plane with one or more figures such that the figures fill the plane with no overlaps and no gaps. Here are a few examples.
Tessellations can also be much more complicated. Here are a couple of examples.
Tessellate the quadrilateral below.
To tessellate any image you will need to reflect and rotate the image so that the sides all fit together. First, start by matching up each side with itself around the quadrilateral.
This is the final tessellation. You can continue to tessellate this shape forever.
Now, continue to fill in around the figures with either the original or the rotation.
Determining if an Object Tessellates
Does a regular pentagon tessellate?
Applying Knowledge about Tessellations
How many squares will fit around one point?
Earlier Problem Revisited
How many regular hexagons will fit around one point?
Does a regular octagon tessellate?
Will the given shapes tessellate? If so, how many do you need to fit around a single point?
- A regular heptagon
- A rectangle
- A rhombus
- A parallelogram
- A trapezoid
- A kite
- A regular nonagon
- A regular decagon
- A completely irregular quadrilateral
- In general, which regular polygons will tessellate?
- Use equilateral triangles and regular hexagons to draw a tessellation.
- The blue shapes are regular octagons. Determine what type of polygon the white shapes are. Be as specific as you can.
- Draw a tessellation using regular hexagons.
- Draw a tessellation using octagons and squares.
- Make a tessellation of an irregular quadrilateral using the directions from Example A.
To view the Review answers, open this PDF file and look for section 12.7.