# What are tessellations in math

Tessellations

A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps. A tessellation is a pattern of shapes repeated to fill a plane. The shapes do not overlap and there are no gaps. The figure above composed of squares is a tessellation since the are no gaps or overlaps between any 2 squares. The figure above composed of regular pentagons is not a tessellation since there are gaps between the tessellations in grey.

A tessellation is a pattern of shapes repeated to fill a plane. The shapes do not overlap and there are no gaps. Tessellations are something we often see in quilts, carpets, floors, and more. In the figure below are three examples. The shape that is repeated, or tessellated, is called a motif. The following are the motifs for the tessellations above.

This is true for any vertex in the tessellation. A regular tessellation is made up of regular congruent polygons. There are only three tessellations that are composed entirely of regular, congruent polygons. A semi-regular tessellation is a tessellation that is composed of two or more regular polygons such that the arrangement of the polygons is the what does the word superior mean for each vertex in the tessellation.

The pattern around each vertex is identical. We call this pattern the order of the vertex of the tessellation, and name it based on the number of sides of each regular polygon surrounding the vertex. The order of the semi-regular tessellation composed of equilateral triangles, squares, and regular hexagons shown above is Start with the polygon with the fewest number of sides first, then rotate clockwise or counterclockwise and count the number of sides for the successive polygons to complete the order.

A non-regular tessellation is a tessellation that is composed of other shapes that may or may not be polygons. The figure above composed of squares is a tessellation since the are no gaps or overlaps between any 2 squares. The figure above composed of regular pentagons is not a tessellation since there are gaps between the tessellations in grey.

The figure above composed of regular octagons is not a tessellation since there is overlap between consecutive octagons in grey. Triangular tessellation.

Each polygon is a non-overlapping equilateral triangle. What are tessellations in math hexagons and equilateral triangles tessellate around each vertex in the order of Regular hexagons, equilateral triangles, and squares tessellate around each vertex in the order of Regular octagons and squares tessellate around each vertex in the order of Regular square and equilateral triangles tessellate around each vertex in the order of Regular dodecagonshexagons, and squares tessellate around each vertex in the order of Regular dodecagons and equilateral triangles tessellate around each vertex in the order of Equilateral triangles and squares tessellate around each vertex in the order of

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Illustrated definition of Tessellation: A pattern made of one or more shapes: the shapes must fit together without any gaps the shapes. A tessellation is the tiling of a plane using one or more geometric shapes such that there are no overlaps or gaps. In other words, a tessellation is a never-ending pattern on a flat 2-D surface (such as a piece of paper) where all of the shapes fit together perfectly like . Apr 11,  · A tessellation is a regular pattern made up of flat shapes repeated and joined together without any gaps or overlaps. These shapes do not all need to be the same, but the pattern should repeat. Another word for tessellation is tiling. Here are some tessellation examples.

A tessellation is a regular pattern made up of flat shapes repeated and joined together without any gaps or overlaps. These shapes do not all need to be the same, but the pattern should repeat. Another word for tessellation is tiling. The word tessellation is derived from the Greek "tesseres", which means "four" and refers to the four sides of a square, the first shape to be tiled.

A regular tessellation is a pattern made by repeating a regular polygon. A regular polygon is one having all its sides equal and all it's interior angles equal. So there are only 3 kinds of regular tessellations - ones made from squares, equilateral triangles and hexagons. Where the shapes join together, the corner point, we call that the vertex. By looking at the vertex and counting the sides of all the shapes that meet at the vertex you are able to name a tessellation.

Choose a vertex and count the sides of the polygons that touch it. In the example above of a regular tessellation of hexagons, next to the vertex are three polygons and each has six sides, so this tessellation is called " 6. A semi-regular tessellation is made of two or more regular polygons e.

The pattern at each vertex should be the same. There are also demi-regular tessellations or polymorph tessellations , but they are difficult to define. Some have described them as a tilings of the 3 regular and 8 semi-regular tessellations, but this is not a very precise definition.

Here are some tessellation examples Regular Tessellations A regular tessellation is a pattern made by repeating a regular polygon. For example Semi-Regular Tessellations A semi-regular tessellation is made of two or more regular polygons e. There are only 8 semi-regular tessellations Other Tessellations There are also demi-regular tessellations or polymorph tessellations , but they are difficult to define.

And some people allow for tessellations of curved shapes. The above exampe of the tessellated lizards was done by famous artist MC Escher. All rights reserved.

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