Creating a shape on a plane or flat surface from a series of common shapes is called a tessellation. Tessellations are often used in art to make interesting designs; M.C. Escher is one artist who used tessellations in his work. When you make a hexagon from a series of diamonds, you are making a tessellation.
To make a hexagon, you must use diamonds with two obtuse and two acute angles. Diamonds with interior 90 degree angles cannot be used to make a hexagon.
Label the interior angles of all three diamonds. Label the two obtuse angles A and label the two acute angles B. An obtuse angle is greater than 90 degrees and an acute angle is less than 90 degrees.
Place the first diamond upright in front of you so one of the acute angles, labeled B, is pointing toward you and the other acute angle is pointed away from you.
Place one of the other diamonds to the left of the first diamond so one of the flat sides of the first diamond is lined up with one of the flat sides of the second diamond. One of the "A" angles of the second diamond should touch the right hand "A" angle of the first diamond and one of the second diamond's "B" angles should touch a "B" angle on the first diamond.
Turn the third diamond on its side so one "A" angle is pointing toward you and one "A" angle is pointing away from you. Slide this diamond into the slot at the bottom of the two other diamond shapes. The "A" on the third diamond should join the two connected "A"s on the first and second diamond and the "B"s on the third diamond should match up with the "B"s on both the first and the second shapes. The outside border completes the hexagon.
- hexagone image by Unclesam from Fotolia.com