#TRIANGLE TESSELLATION TEMPLATE HOW TO#

Work on the following exercises on your own or with a partner. Explain why regular pentagons will not tessellate.Use angles to explain why regular hexagons will tessellate.Use the fact that the sum of the angles in any quadrilateral is 360° to explain why every quadrilateral will tessellate.Repeat this process with each of the other tiles.Can you use many copies of a single triangle to tessellate the plane? Can you fit the squares together in a pattern that could be continued forever, with no gaps and no overlaps? Can you do it in more than one way? In each problem, focus on just a single tile for making your tessellation. You will need lots of copies (maybe 10–15 each) of each shape below. Work on these exercises on your own or with a partner. Tessellations are often called tilings, and that’s what you should think about: If I had tiles made in this shape, could I use them to tile my kitchen floor? Or would it be impossible? On Your Own The first two tessellations above were made with a single geometric shape (called a tile) designed so that they can fit together without gaps or overlaps.

#TRIANGLE TESSELLATION TEMPLATE HOW TO#

So we’ll focus on how to make symmetric tessellations. It’s actually much harder to come up with these “aperiodic” tessellations than to come up with ones that have translational symmetry. The Penrose tiling shown below does not have any translational symmetry. Many tessellations have translational symmetry, but it’s not strictly necessary. The idea is that the design could be continued infinitely far to cover the whole plane (though of course we can only draw a small portion of it). Geometry in Art and Science TessellationsĪ tessellation is a design using one ore more geometric shapes with no overlaps and no gaps.

Triangle tessellation template