Mostly true - you cannot tessellate only regular pentagons in two dimensions, since you cannot sum up the intersection of the angles to 360 degrees. If you tessellate a regular pentagon in three dimensions, you end up with a dodecahedron.
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No.
True
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.
All regular polygons whose interior angles are a factor of 360 degrees will tessellate with themselves
Any polygon with external angles which are equal to a factor of 360 will tessellate. The only regular polygons which will tessellate are equilateral triangles, squares, and hexagons.