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No.
Yes. Any triangle will tessellate.
Triangle, square and hexagon
All of them can be used.Any triangle or quadrilateral will tessellate. There are 15 classes of irregular convex pentagons which will tessellate. Regular hexagons and 32 classes of irregular convex hexagons will tessellate. There are also concave pentagonal and hexagonal shapes which will tessellate.
Equilateral triangle, square and regular hexagon.