Filling the Plane

After M. C. Escher, "Plane-filling Motif with Reptiles", 1941 woodcut. The woodcut doesn't seem anywhere near precise enough to tile the plane with. I know, he undoubtedly worked it out more precisely in another work. I believe I've seen it. But I'm trying to work back to his intent from this rough sketch, just for fun. It appears the basic plan is hexagonal. At any node where the two lizards coincide nose-to-tail, there should actually be three incident tails alternating with three incident noses. Edges joining those nodes divide the plane up into equilateral triangles, each containing three half-lizards. Or so I suspect.