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When a regular polygon can tessellate, it can be placed around a point (which has an angle of 360 degrees) with no 'space' left over. However some regular polygons don't tessellate because their interior angle is not a factor of 360 (does not go into 360 equally), meaning that there will be 'space' left over or it will overlap. To check if a regular polygon can tessellate, see if it's interior angle goes into 360 equally. (360/interior angle), if it does, it will tessellate and if it doesn't it's because the interior angle is not a factor of 360 meaning it will not fit round a point and won't tessellate.
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Does an even numbered sided shape tessellate?
Some do, some don't. For regular tessellation, you require the interior angles to be a factor of 360 degrees. An octagon will not tessellate. On the other hand a triangle, which does not have an even number of sides, will.
Is it true you can not tessellate six sides polygon by itself?
No, it is not true that you cannot tessellate a six-sided polygon by itself. Hexagons are a type of polygon that can tessellate, which means they can be arranged in a repeating pattern to completely cover a plane without any gaps or overlaps.
Is it possible to tile a floor with copies of a regular polygon?
Yes, but only with some polygons.
Why can only some shapes tessellate?
Shapes can tessellate only if a number of them can meet at a point and cover 360 degrees without overlap. For regular shapes this requires that the angles of the shape are a factor of 360 degrees. For non-regular shapes it is necessary that the angles of the shapes can be grouped so that they sum to 360 degrees.
How 3D shape tessellate?
Some 3D shapes will tessellate as for example a brick wall
