# Why does a regular octagon not tessellate?

## Why does a regular octagon not tessellate?

Each angle in a regular pentagon is 1080 ∘ ÷ 8 = 135 ∘ . From this, we know that a regular octagon will not tessellate by itself because does not go evenly into .

**What regular shapes can tessellate?**

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

**Do Dodecagons tessellate?**

We can see from this that the pentagon, hexagon, octagon, and dodecagon tesselate with one skipped vertex. The corresponding holes are shaped decagon, hexagon, square, and triangle.

### Can an irregular octagon tessellate?

No, a regular octagon cannot tessellate.

**Is it possible to use only an octagon to create a tessellation?**

It is not possible to tile the plane using only octagons. Two octagons have angle measures that sum to 270° (135° + 135°), leaving a gap of 90°.

**Do all Pentominoes tessellate?**

Any one of the 12 pentominoes can be used as the basis of a tessellation. With most of them (I, L, N, P, V, W, Z) it is easy to see how it can be done. But the F, T, U and X are a little more difficult and, if you are not careful, you will soon find ‘holes’ in your tessellation.

#### Do Nonagons tessellate?

Answer and Explanation: No, a nonagon cannot tessellate the plane. A nonagon is a nine-sided polygon.

**Do Heptagons tessellate?**

Regular heptagons, of course, can’t tile a plane by themselves. Of all tessellations of the plane which include regular heptagons, I think this is the one which minimizes between-heptagon gap-size (the parts of the plane outside any heptagon).

**How do you tell if a shape can be tessellated?**

How do you know that a figure will tessellate? If the figure is the same on all sides, it will fit together when it is repeated. Figures that tessellate tend to be regular polygons. Regular polygons have congruent straight sides.

## What are the three rules for tessellations?

REGULAR 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 polygon Cannot be used to form a regular tessellation?**

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°.