Kites! They're 1/6 of a hexagon but split through the flat sides rather than the corners, making the most interesting and beautiful fussy cut designs. Kites are measured along the short sides. Six 1" kites go together to make a 2" hexagon.
Kites are the base shape for the lovely Rose Star block, and make funky triangles if all the short sides point in. They are also used in the Waterwheel quilt with Equilateral Triangles.