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It's possible to create a regular tesselation with a regular octagon?
No.
Is it possible to create a tesselation using only regular pentagons?
No because each interior angle is 108 degrees which is not a factor of 360 degrees
Why cant a regular pentagon be used to create a regular tessellation?
it can tessellate * * * * * NO IT CANNOT! A regular polygon can be used to create a regular tesselation if and only if its interior angle divides 360 degrees. The interior angle of a regular pentagon is 108 degrees, which does not divide 360 degrees so it cannot be used for a regular tesselation. . Three pentagons meeting at a point would cover 3*108 = 324 degrees - not enough to cover the 360 degrees at a point. Meanwhile 4 pentagons would cover 4*108 = 432 degrees - resulting in a 72 degree overlap.
Which polygon does not tessellate and why?
Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation. However, for polygons with any number of sides, there are irregular versions that can tessellate.
Is it possible to create a regular tessellation with a regular octagon and an equilateral triangle?
yes
