## What are the only three regular polygons that can be used when creating a tessellation?

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.

What are the 3 basic tessellation shapes?

There are three regular shapes that make up regular tessellations: the equilateral triangle, the square and the regular hexagon.

### What is a three sided regular polygon called?

triangle
A three-sided polygon is a triangle.

Does a regular polygon have 3 sides?

A regular polygon having 3 sides is known as an equilateral triangle.

#### What 3 polygons can tessellate?

Only three regular polygons (shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons.

Why do only 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 are the 3 rules to tessellate?

Tessellations

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

What shapes will not tessellate?

Shapes That Do Not Tessellate Circles or ovals, for example, cannot tessellate. Not only do they not have angles, but you can clearly see that it is impossible to put a series of circles next to each other without a gap. See? Circles cannot tessellate.

### What is a uneven four sided shape called?

Quadrilaterals are polygons with four sides (hence the beginning “quad”, which means “four”). A polygon with non-equal sides is called irregular, so the figure that you are describing is an irregular quadrilateral. This figure has side lengths of 1, 2, 3, and 4 respectively, so it is an irregular quadrilateral.

Is any 3 sided polygon a triangle answer?

A polygon with three sides is a triangle. Notice the use of the little triangle next to the vertices to indicate we are referring to the triangle instead of the angle. A polygon with four sides is a quadrilateral.

#### What is a 6 sided shape called?

hexagon
In geometry, a hexagon (from Greek ἕξ, hex, meaning “six”, and γωνία, gonía, meaning “corner, angle”) is a six-sided polygon or 6-gon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

Can circles tessellate?

Circles are a type of oval—a convex, curved shape with no corners. While they can’t tessellate on their own, they can be part of a tessellation… but only if you view the triangular gaps between the circles as shapes.

## Are there any regular polygons that can tessellate the plane?

In Tessellations: The Mathematics of Tiling post, we have learned that there are only three regular polygons that can tessellate the plane: squares, equilateral triangles, and regular hexagons. In Figure 1, we can see why this is so. The angle sum of the interior angles of the regular polygons meeting at a point add up to 360 degrees.

How is a triangle represented as a regular tessellation?

Using this notation, the triangular tessellation can be represented as since a triangle has 3 sides and 6 vertices meet at a point. In the proof, as shown in Figure 1, we are going to show that the product of the measure of the interior angle of a regular polygon multiplied by the number of vertices meeting at a point is equal to 360 degrees.

### Are there any regular polygons with less than three sides?

Since there are no regular polygons with less than three sides, the only regular polygons which will tile be themselves are triangles, squares, and hexagons.

Why are there no gaps in a quadrilateral tessellation?

Since the angle sum of the quadrilateral is 360°, the angles close up, the pattern has no gaps or overlaps, and the quadrilateral tessellates. Recall from Fundamental Concepts that a convex shape has no dents. All triangles are convex, but there are non-convex quadrilaterals.