The diamonds in hat I call a LeMoyne star have equal sides and 45-135-45-135 angles in them.
One could also do some interesting things with the 60-120-60-120 degree diamonds.
GingerK's suggestion to just lay them out and see what happens is a good one. I think one could maybe add dark navy strips for that stained glass effect to define the triangles and or diamonds.
From the picture, the triangles look like they might be 60-60-60 degree ones - and there are a zillion possibilities using those triangles. Measure them and see.