Notice how every vertex you point to is surrounded by three hexagons (six sides). Find a corner, or a vertex, and look at all the polygons meeting at this spot. Tessellation Rule #3: Every vertex has to look the same.Ī vertex is where all the corners of each polygon meet.įor example, look at each corner of our tile floor. In order to make a tessellation, we must use one or more regular polygons with no overlapping and no gaps. However, you could make a tessellation with octagons and squares! No overlapping and no gaps! This 8-sided shape would overlap with each other. This is also true if there were gaps between tiles.įor example, you couldn't make a tessellation with just octagons. The floor wouldn't look right or be smooth to walk on if the edges of the tiles overlapped. Tessellation Rule #2: The polygons can't overlap or have gaps in the pattern. In order to make a tessellation, we must use regular polygons! This tile floor is a tessellation made out of all regular hexagons! Here are examples of other regular polygons labeled by their number of sides:Įach of these polygons is made up of sides that are the same length. For example, a square is a regular polygon because all four sides are the same length. The names of polygons tell you how many sides the shape has.Ī regular polygon is when all the sides are equal length. Tessellation Rule #1: The shapes must be regular polygons.Ī polygon is any shape that is formed by straight lines. The polygons can't overlap or have gaps in the pattern. Whew! That seems complicated! But just like our shape pattern from above, we can break this pattern down into three simple rules to follow. This is an example of a tessellation.Ī tessellation is a type of pattern that covers an entire flat surface with repeating polygons without any gaps or overlapping. The tiles cover an entire flat area and are made up of one or more shapes. I bet you can find a floor or a wall with tiles on it similar to this one. We see patterns all around us in our lives. If we follow these rules, we can guess what the next shape in the pattern will look like! The next shape will be a small green circle! These three rules make the pattern we see above.
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