You would not be able to create a tessellation with an octagon right?

Question

Mathematics

Joanna Roy

20 September, 23:23

You would not be able to create a tessellation with an octagon right?

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Kianna Ritter · Answer 1

Yes you are correct. An octagon cannot tessellate the plane. The reason why is because the interior angle is 135 degrees which is not a factor of 360. Trying to line up the angles will have overlap of the polygons. A tessellation happens when there are no gaps or overlaps of the polygons (think of a tile floor).

Contrast this with a regular hexagon which has an interior angle of 120 degrees, or an equilateral triangle with an interior angle of 60 degrees. Both 120 and 60 are factors of 360, so this shows that a regular hexagon and an equilateral triangle can be used to tessellate the plane.