Here's M.C. Escher's "Hexagon Trick" for constructing an interesting tessellation based on the (6,3) Euclidean tessellation.

Summary: [br][br] The goal is to produce three 120 degree angles on each of the edges of triangle ABC.[br][list=1][*]Start with any triangle ABC[/*][*]Rotate(B, 30°, A) and rename B' (if needed)[br][/*][*]Rotate(A, -(30°), B) and rename A' (if needed)[/*][*]Intersect(Segment(A,B'),Segment(B,A')) and rename D (if needed)[/*][*]Rotate(C, 30°, B) and rename C' (if needed)[/*][*]Rotate(B, -30°, C) and rename B'_1 (if needed)[/*][*]Intersect(Segment(B, C'), Segment(C, B'_1)) and rename E (if needed)[/*][*]Rotate(A, 30°, C) and rename A'_1 (if needed)[/*][*]Rotate(C,-30°,A) and rename C'_1 (if needed)[/*][*]Intersect(Segment(A, C'_1), Segment(C, A'_1)) and rename F (if needed)[/*][*]Hide all the points with a prime on them[/*][*]Polygon(A,D,B,E,C,F) and rename it poly1 (if needed)[/*][*]Sequence(Rotate(poly1,k*120°,D),k,1,2)[br][/*][*]Sequence(Rotate(poly1,k*120°,E),k,1,2)[br][/*][*]Sequence(Rotate(poly1,k*120°,F),k,1,2)[br][/*][/list][br]Note: You can add polylines to AD, BE and CF as in the triangle trick, and rotate them 120 degrees around D, E and F, respectively to increase the complexity of your tessellating shape.