Geometry Center: Triangle Tilings and Polyhedra (Science U)

Triangle Tilings: Making Patterns

Triangle Tiling refers to the process of taking many copies of a single triangle and laying them next to each other to fill out an area. We make the pattern by laying down one triangle first, then reflecting that triangle in imaginary mirrors on the the triangle's edges. For example, if we use a tile shaped like this

and put lots of copies next to each other, we end up with a pattern like this:

The coloring pattern that we're using divides the original triangle into 3 colored regions of purple, yellow, and green. As we move the point where these three regions meet, we change the color pattern, and we get different patterns in the resulting tiling. Here are a few of the variations that are possible:

[triangle tiling]

You can make your own patterns like the ones above using the Science U interactive or read on about why the shape of the original triangle is important and about how allowing the triangle to bend gives rise to 3D shapes!