Which shapes can tessellate?

Which shapes can 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?

Why can a regular hexagon tessellate?

A shape will tessellate if its vertices can have a sum of 360˚ . In an equilateral triangle, each vertex is 60˚ . Similarly, a regular hexagon has an angle measure of 120˚ , so 3 regular hexagons will meet at a point in a hexagonal tessellation since 3×120˚=360˚ .

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 does a hexagon 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°.

What is tessellation hexagon?

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. The internal angle of the hexagon is 120 degrees so three hexagons at a point make a full 360 degrees. It is one of three regular tilings of the plane.

How do you tell if a shape can tessellate?

Regular polygons tessellate if the interior angles can be added together to make 360°.

1. A square has an interior angle of 90°, so 4 squares fit together to make 360°: 360 ÷ 90 = 4.
2. An equilateral triangle has an interior angle of 60°, so 6 triangles fit together to make 360°: 360 ÷ 60 = 6.

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!