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Why can't a regular octagon tessellate?

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In order for a regular polygon to be able to tessellate, each of its interior angles x must be a factor of 360 ∘ . When this happens, you can place k = 360 x of these regular shapes meeting at a single point; you'll end up with a neat 360 ∘ angle at this point, and the shapes will tessellate. read more

In order for a regular polygon to be able to tessellate, each of its interior angles [math]x[/math] must be a factor of [math]360^\circ[/math]. When this happens, you can place [math]k=\dfrac{360}{x}[/math] of these regular shapes meeting at a single point; you'll end up with a neat [math]360^\circ[/math] angle at this point, and the shapes will tessellate. read more

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. read more

A polygon will tessellate if the angles are a divisor of 360. 128.57 is not a divisor of 360. The only regular polygons that tessellate are Equilateral triangles, each angle 60 degrees, as 60 is a divisor of 360. A regular quadrilateral (square), each angle is 90 degrees, as 90 is a divisor of 360. read more

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Why can't a regular octagon tessellate
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