Can a 8 sided shape tessellate?

Answer 1

an interior angle of a regular octagon is 135 degrees

since 360/135 is not an integer, a regular octagon cannot be tessellated.

also, other octagons cannot be tessellated.

the total interior angle sum of an octagon is 1080 degrees.

however, 1080 cannot be written as a sum of eight numbers which can divide 360 and result as an integer (i.e. 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360) (of course you cannot form a polygon with an angle of 180 or 360 degrees)

the only possible tessellations using polygons of the same kind are as follows: triangles, quadrilaterals ans hexagons.