Hexiamonds and dodecahexes
Since one hexagon can be cut into six triangles with the same edge length, all dodecahexes (shapes comprising 12 hexagons) would have an area of 72 triangles. This is precisely the area of the whole set of hexiamonds. George Sicherman's calculations show that there are exactly 310 such dodecahexes. You can admire them on his website. Some of them are well known and highly symmetrical.
