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The angles of a n-sided regular polygon have the measure of (n-2)*180/n degrees.
A regular octagon's angle has (8-2)*180/8 = 6*180/8 = 135 degrees.
If you stick together two sides of two different (but congruent) regular octagons you get one downward and one upward. We can say this without loss of generality because up and down are just perspective that you can change as you look around the construction.
So, at the left of the common side you have two angles around the vertexes. Both of the angles have 135 degrees (being angles of regular octagons). But there is a third angle. The sum of the measures of angles around a point is 360 degrees. So the third angle has 360-135-135 = 90 degrees. And the two sides that form the angle are congruent. ==> you construct a square.
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Can a octagon and a square tessellate together?
no
Does an octagon tessellate?
An octagon cannot tessellate because when you put about 4 together, there are gaps in between the shapes, which is not allowed in a tessellation. When you put together 5 octagon's, some of them are overlapping and there still are gaps. Therefore, an octagon cant tessellate.
Can an octagon tessellate?
An octagon can be used to create a tessellation, but an octagon cannot tessellate on its own.
Can an octagon and square tessellate?
Yes - because, when you lay regular octagons together so they're touching, the space between the octagons is a perfect square.
Will an octagon tessellate?
A regular octagon will not tessellate but an irregular one can.
