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To be able to tessellate where a vertex meets other vertices, the total of those angles must be a full circle of 360°. The interior angle of an Octagon is 135° which does not divide into 360° which means there cannot be a complete number of vertices meeting and so it cannot, by itself, tessellate.
However, two octagons meeting at a point would have 135° + 135° = 270° leaving 90° which is the interior angle of a square. So octagons and squares together will tessellate.
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ReneA regular octagon cannot tessellate because the interior angles of an octagon are 135 degrees, which does not evenly divide into 360 degrees, the total angle around a point. In order for a shape to tessellate, the sum of the interior angles must evenly divide into 360 degrees. Since the interior angles of a regular octagon do not meet this criterion, it cannot tessellate without gapping or overlapping.
Do octagons tessellate?
No it does not tessellate you have to pentagons in order for it to tessellate. * * * * * It is not at all clear what "have to pentagons" has to do with this. No polygon with 7 or more sides will tessellate. Octagons will tessellate if mixed with squares but that is not "proper" tessellation since it involved more than one shape.
Can a octagon tessellate?
YES
Can a regular octagon and a square tessellate?
You cannot use a regular octagon on it's own to make a tiling pattern without any gaps. However a regular Octagon and a square can be used together to make a tessellation. Many people think that regular octagons tesselate on their own because they do not appreciate the need for no gaps.
Can you tessellate eight sided regular polygons by themselves?
No, they will not fit together, you will also need a square with sides equal in length to the sides of the octagon.
Does regular heptagon tessellate?
True * * * * * No. The only regular polygons that will tessellate are a triangle, a square and a heagon. So a regular heptagon will not tessellate.
