His art is enjoyed by millions of people all over the world. Maurits Cornelis Escher (1898-1972) is a graphic artist known for his art tessellations. "Designs featuring animals, birds, etc, which can fill the page, without over-lapping, to form a pattern." "A collection of plane figures that fills the plane with no overlaps and no gaps." "To form into a mosaic pattern, as by using small squares of stone or glass." This is named a 4.8.8 tessellation."A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps." Let's check to see if every vertex is the same.Įach vertex is surrounded by a square (four sides) and two octagons (eight sides). Now, look at our example of a tessellation made out of squares and octagons. 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. The last rule of the pattern is that the sizes of the shapes are small, small, big.This rule also repeats over and over again to make a pattern. The second rule in this pattern is that the type of shape changes from a circle, to a star, and back to a circle.The rule repeats over and over again to make the pattern. The first rule in this pattern is that the color of the shapes are green, then blue, then orange.You can find patterns with colors, shapes, numbers, and more! For example, this row of shapes has a pattern: Let's get started by looking closely at these tile floors.īut before we try to understand tessellations, we need to remember how patterns work!Ī pattern is something repeated with a set of rules.
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