If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.
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Yes.
Yes.
An [equilateral] triangle, square and hexagon are the only regular polygons which, by themselves, will tile a surface.
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Triangles, squares and hexagons. That is if they all have to be the same. If you use different regular polygons, you can tile a flat surface with triangles and 12-sides or with squares and 8-sides for example.