![]() 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: ![]() "Demiregular Tessellation."įrom MathWorld-A Wolfram Web Resource.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. Referenced on Wolfram|Alpha Demiregular Tessellation Cite this as: Geometrical Foundation of Natural Structure: A Source Book of Design. "Die homogenen Mosaike -ter Ordnung in der euklidischen Ebene. There are 20 such tessellations, illustrated above, as first enumerated by Krötenheerdt (1969 Grünbaum and Shephard 1986, pp. 65-67). Caution is therefore needed in attempting to determine what is meant by "demiregularĪ more precise term of demiregular tessellations is 2-uniform tessellations (Grünbaum and Shephard 1986, p. 65). However, not all sources apparently give the sameġ4. (which leads to an infinite number of possible tilings). Tessellations (which is not precise enough to draw any conclusions from), while othersĭefined them as a tessellation having more than one transitivity class of vertices Some authors define them as orderly compositions of the three regular and eight semiregular A demiregular tessellation, also called a polymorph tessellation, is a type of tessellation whose definition is somewhat problematical. ![]()
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