# What Are the 3 Types of Tessellations?

October 17, 2022

There are three types of regular tessellations: triangles, squares, and hexagons.

## What are the 3 basic tessellation shapes?

There are three regular shapes that form regular tessellations: the equilateral triangle, the square, and the regular hexagon. For example, a regular hexagon is used in the pattern of a honeycomb, the honey bee’s nesting structure.

## What are the 3 rules to tessellate?

• RULE #1: The tessellation must tile a floor (going on forever) with no overlaps or gaps.
• RULE #2: The tiles must be regular polygons – and all the same.
• RULE #3: Every vertex must look the same.

## What is examples of tessellation?

Examples of tessellations include: a tiled floor, a brick or log wall, a chess or checker board, and a fabric pattern. A tessellation is a tiling over a layer containing one or more figures so that the figures fill the layer with no overlaps or gaps.

## What only 3 shapes can tessellate?

Only three regular polygons (shapes where all sides and angles are equal) can form a tessellation on their own – triangles, squares and hexagons.

## What are the 3 ways a tessellation can be placed when creating the design?

There are only three shapes that can form such regular tessellations: the equilateral triangle, the square, and the regular hexagon.

## What are 3 ways to transform shapes to create tessellations?

• Types of transformations:
• Line symmetry – the shape(s) are “flipped”.
• Rotational symmetry – the shape(s) are “rotated”.
• Translation – the shape(s) is “pushed”.

## How do you identify a tessellation?

How do you know a character is tessellated? If the figure is the same on all sides, it will fit together when repeated. Figures that tessellate are usually regular polygons. Regular polygons have congruent even sides.

## How do you name a tessellation?

To name a tessellation, simply work your way around a vertex, counting the number of sides of the polygons that make up that vertex. The trick is to circle the vertex so that the smallest possible numbers appear first. That’s why we wouldn’t call our 3, 3, 3, 3, 6 tessellation 3, 3, 6, 3, 3!

## How many regular tessellations are there?

First, there are only three regular tessellations, namely triangles, squares, and hexagons. To create a regular tessellation, the interior angle of the polygon must divide by 360. This is because the angles must add up to 360 so there are no gaps.

## What tessellate means?

Definition of tessellate

verb transitive : to shape or decorate with mosaic.

## Is tessellation math or art?

Tessellations are both mathematics and art. I think because you need knowledge of math like rotation, translation, reflection, names of shapes and more to create a tessellation, but it also involves elements of art. Line, Shape, Color, Value, Form and Texture…

## Is circle a tessellation?

A pattern of shapes that fit together seamlessly is called tessellation. So squares form a tessellation (a rectangular grid), but circles don’t. Tessellations can also consist of more than one shape as long as they fit together seamlessly.

## Why are there only 3 regular tessellations?

What regular polygons can be tessellated without gaps or overlaps? Equilateral triangles, squares, and regular hexagons are the only regular polygons that can be tessellated. Therefore there are only three regular tessellations.

## Which figure Cannot tessellate?

For example,

circles or ovals cannot be tessellated. Not only do they have no corners, but you can clearly see that it’s impossible to put a series of circles together without a gap.

## Do all triangles tessellate?

Tessellate all triangles. The picture works because all three corners (A, B, and C) of the triangle come together to form a 180° angle—a straight line. This property of triangles will be the basis of our study of polygon tessellations, so we state it here: The sum of the angles of a triangle is 180°.

## What are two examples of tessellations that are found in everyday objects?

Art, architecture, hobbies and many other areas contain examples of tessellations found in our everyday environment. Specific examples are oriental carpets, quilts, origami, Islamic architecture and the works of M.C. Escher. Oriental carpets contain tessellations indirectly.

## What is the purpose of tessellations?

Tiles used in tessellations can be used to measure distances. Once students know how long the sides of the different tiles are, they can use the information to measure distances. The tiles could be used to talk about scope.

## How do you solve tessellations?

### References:

1. https://www.livescience.com/50027-tessellation-tiling.html
2. https://www.coolmath4kids.com/more/tessellations
3. https://www.ck12.org/book/ck-12-geometry-concepts/section/12.7/
4. https://www.mathnasium.com/2016/02/math-is-beautiful-tessellations
5. https://en.wikipedia.org/wiki/Tessellation
6. https://www.learnalberta.ca/content/mejhm/html/object_interactives/transformations/flashHelp/pdf/Tessellations_Math_Help.pdf
8. https://www.coolmath.com/lesson-tessellations-4
9. https://nrich.maths.org/semiregular/solution
10. https://www.merriam-webster.com/dictionary/tessellate
11. https://www.scis-china.org/community/news/news-details/~board/news-stories/post/tessellations-math-or-art
12. https://topdrawer.aamt.edu.au/Patterns/Misunderstandings/Tessellations