# Can you tile with equilateral triangle?

Because the area of the triangle has to be a multiple of the area of the tile, the triangle must have side length divisible by 5 (where 1 is the length of the short edges of the tile). The analogous tile made of three equilateral triangles can tile any equilateral triangle with side length divisible by three.

Table of Contents

## Can you tile with equilateral triangle?

Because the area of the triangle has to be a multiple of the area of the tile, the triangle must have side length divisible by 5 (where 1 is the length of the short edges of the tile). The analogous tile made of three equilateral triangles can tile any equilateral triangle with side length divisible by three.

### Which regular polygon Cannot be used for a tiling?

There are no whole numbers between 2 and 3, so no regular polygon with more than eight sides can form a regular tiling. Alas, we have solved our problem! There are only three regular poly- gons that form a regular tiling: equilateral triangles, squares, and regular hexagons.

**Is it possible to create a regular tiling using only regular pentagons?**

A regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a regular pentagon, 108°, is not a divisor of 360°, the angle measure of a whole turn.

**Can a regular pentagon tile the plane?**

The regular pentagon cannot tile the plane. (A regular pentagon has equal side lengths and equal angles between sides, like, say, a cross section of okra, or, erm, the Pentagon). But some non-regular pentagons can.

## Can a Dodecagon be used to tile a flat surface?

There are exactly eight ways to do this using various combinations of regular polygons—triangles, squares, hexagons, octagons, and dodecagons (twelve-sided polygons). Any of these eight combinations would make a nice floor tiling.

### Do all triangles make tiling patterns?

The simplest polygons have three sides, so we begin with triangles: All triangles tessellate. The picture works because all three corners (A, B, and C) of the triangle come together to make a 180° angle – a straight line.

**Would an octagon and equilateral triangle tessellate?**

Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate.

**Do all polygons fit together?**

Out of all the regular polygons there are only three you can use to tile a wall with: the square, the equilateral triangle, and the regular hexagon. All the others just won’t fit together.

## Can you tessellate a triangle and pentagon together?

Since each triangle has angle sum 180° the angle sum of the pentagon is 180° + 180° + 180° = 540°….Tessellations by Convex Polygons.

Sides | Angle Sum | Tessellates? |
---|---|---|

3 | 180° | Yes. All triangles tessellate. |

4 | 360° | Yes. All quadrilaterals tessellate. |

### Can you tessellate a regular pentagon?

‘Tiling the plane’ means that identical copies of a shape can be repeatedly used to fill a flat surface without any gaps or overlays. This is also called tessellation. Fifteen different types of pentagon can tessellate, but the regular pentagon cannot.

**Why regular pentagons do not tessellate?**

We have already seen that the regular pentagon does not tessellate. A regular polygon with more than six sides has a corner angle larger than 120° (which is 360°/3) and smaller than 180° (which is 360°/2) so it cannot evenly divide 360°.

**Which polygons can tile a 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.