# What geometric shapes will tessellate?

## What geometric shapes will tessellate?

Only three regular polygons (shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons. What about circles? Circles are a type of oval—a convex, curved shape with no corners.

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How do you do a geometric tessellation?

1-Step Cutting Tessellation

1. Take one square piece of paper and cut a weird shape out of one side of the square.
2. Line your oddly-shaped cut-out on top of a second square of paper, lining up the long edges.
3. Repeat for each of the remaining three squares.
4. Take one of your squares and cut out your tracing.

### What basic shapes can be used in tessellation?

There are only three shapes that can form such regular tessellations: the equilateral triangle, square and the regular hexagon. Any one of these three shapes can be duplicated infinitely to fill a plane with no gaps.

What is a pure tessellation?

If you use one regular polygon (sides are equal in length and interior angles are congruent), such as a square, to cover a plane without any gaps or overlapping, then it is called a pure or regular tessellation, and when more than one polygon is used to tessellate a plane, than it is called a semi-regular tessellation.

## What shapes can tessellate and why?

Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. You can have other tessellations of regular shapes if you use more than one type of shape. You can even tessellate pentagons, but they won’t be regular ones. Tessellations can be used for tile patterns or in patchwork quilts!

What is a tessellation in art?

A tessellation, or tiling, is a division of the plane into figures called tiles. The most common tessellations today are floor tilings, using square, rectangular, hexagonal, or other shapes of ceramic tile. Escher’s primary interest in tessellations was as an artist.

### What are the most common tessellations today?

The most common tessellations today are floor tilings, using square, rectangular, hexagonal, or other shapes of ceramic tile. Escher’s primary interest in tessellations was as an artist.

What is non-regular tessellation?

Non-regular tessellation is the one in which there are no restrictions regarding the shapes used or their arrangement around vertices. It is believed there is an infinite number of irregular ones. When observing a completed tessellation, you could notice that the original tile, or a motif, repeats in a pattern.

## Who is the most famous tessellation artist in history?

The most renowned tessellation artist in history, presently still very much adored by mathematicians and the rest, whose production focused on the questions concerning the nature of visual perception, infinity, and patterns is M.C. Escher.