An octagon has an internal angle of 135 degrees.
If we put 2 octagons side-by-side, that makes 2*135=270°, leaving a gap of 90° which does not fit another octagon. Therefore we cannot tessellate with an octagon.
Use the same logic with other regular polygons and you will find that only three regular polygons can tessellate.
Why is it impossible for a regular polygon with more than six sides to tesselate the plane?
I know it has something to do with the angles, but I'm not sure what to write for this. 3 hexagons tesselate the plane and they have angles at 120, but why can't an octagon? Why is it impossible? Thanks.
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