There is an infinite number of such tessellations. Non-regular tessellations are those in which there is no restriction on the order of the polygons around vertices. There are eight semi-regular tessellations which comprise different combinations of equilateral triangles, squares, hexagons, octagons and dodecagons. Semi-regular tessellations are made up with two or more types of regular polygon which are fitted together in such a way that the same polygons in the same cyclic order surround every vertex. There are only three regular tessellations which use a network of equilateral triangles, squares and hexagons. Regular tessellations are made up entirely of congruent regular polygons all meeting vertex to vertex. In geometrical terminology a tessellation is the pattern resulting from the arrangement of regular polygons to cover a plane without any interstices (gaps) or overlapping. Examples range from the simple hexagonal pattern of the bees' honeycomb or a tiled floor to the intricate decorations used by the Moors in thirteenth century Spain or the elaborate mathematical, but artistic, mosaics created by Maurits Escher this century. This is named a 4.8.8 tessellation.Patterns covering the plane by fitting together replicas of the same basic shape have been created by Nature and Man either by accident or design. 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.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |