# BookRiff

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## Why can hexagons tessellate?

A tessellation is a pattern created with identical shapes which fit together with no gaps. Regular polygons tessellate if the interior angles can be added together to make 360°.

## Will a hexagon tessellate itself?

Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate. Therefore, there are only three regular tessellations.

What are two characteristics that make hexagons suitable form for tessellation?

Regular tessellations have interior angles that are divisors of 360 degrees. For example, a triangle’s three angles total 180 degrees; which is a divisor of 360. A hexagon contains six angles whose measurements total 720 degrees. This also is a divisor of 180, because 180 fits evenly into 720.

### What angles are in a hexagon?

A hexagon has six sides, and we can use the formula degrees = (# of sides – 2) * 180. Then degrees = (6 – 2) * 180 = 720 degrees. Each angle is 720/6 = 120 degrees.

### Why do triangles squares and hexagons tessellate?

A shape will tessellate if its vertices can have a sum of 360˚ . In an equilateral triangle, each vertex is 60˚ . Thus, 6 triangles can come together at every point because 6×60˚=360˚ . This also explains why squares and hexagons tessellate, but other polygons like pentagons won’t.

What does a hexagon tessellate with?

Here, the hexagons are further apart, with a line of triangles between them. These tessellations can be made with triangle grids. Dodecagons (12 sides) and triangles – Since the sides of the shapes must be the same length, so they can fit together, you end up with the dodecagons being much larger than the triangles.

## What’s the exterior angle of a hexagon?

60°
We know that the number of sides of a hexagon is, n = 6. By the sum of exterior angles formula, Each exterior angle of a regular polygon of n sides = 360° / n. Answer: Each exterior angle of a regular hexagon = 60°.

What can be used to make a regular tessellation?

In regular tessellations, also known as periodic tessellations, a single shape is used to tessellate. Only equilateral triangles, squares, and hexagons can be used in a regular tessellation.

### What are the characteristics of a regular hexagon?

Properties of a Regular Hexagon All the sides are equal in length. All the interior angles measure 120°. The sum of all the interior angles of a regular hexagon is 720°.

### Can a regular hexagon be tessellated?

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.

What shape can be used to make a regular tessellation?

Tessellation Regular Tessellations. A regular tessellation is a pattern made by repeating a regular polygon. Look at a Vertex A vertex is just a “corner point”. What shapes meet here? So this is called a “6.6.6” tessellation. Semi-regular Tessellations. A semi-regular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same!