Tessellations

This is a Roman inlaid marble tiling pattern

For more see http://www2.spsu.edu/math/tile/historical/roman/

Roman Mosaic

Do all shapes tessellate?

• Triangles?

• Quadrilaterals?

• Pentagons?

• Hexagons?

• Heptagons?

• Octagons?

Triangles always tessellate

Quadrilaterals always tessellate.

There are only three regular tessellations:

Jump to transformations

Activity for the computer:

Start a new PowerPoint Presentation. Save it in your network folder. Make the following slides:

• Slide 1 is the title slide “Tessellations” by Your name. The following slides should all show tessellations in two colours.

Before you start click Draw Grid Snap objects to other objects.Use Autoshapes to select your shape (hold down shift to get the

regular shape)

• Slide 2 is a tessellation of equilateral triangles • Slide 3 is a tessellation of squares• Slide 4 is a tessellation of hexagons

• Slide 5 is a tessellation of Octagons and SquaresAre there any other pairs of regular shapes that tessellate?

Eight semi-regular tessellations

• 3,3,3,4,43,3,3,4,4• 3,6,3,63,6,3,6• 3,3,4,3,43,3,4,3,4• 3,3,3,3,63,3,3,3,6• 4,8,84,8,8• 3,4,6,43,4,6,4• 3,12,123,12,12• 4,6,124,6,12

Semi-regular Tessellations

None edge to edge patterns

Combining shapes

Modifying by translation

Start with a two by three rectangle in your exercise book.

Start with a two by three rectangle in your exercise book.

Cut a section out from the left and add it to the right.

Start with a two by three rectangle in your exercise book.

Cut a section out from the left and add it to the right.

Show, using at least six copies of your shape how it tessellates.