A conformal map projection mapping a sphere or hemisphere into a rhombus having one opposite pair of angles equal to 60° and the other pair equal to 120°. The complex function z(x + iy) is related to longitude l and latitude f on the sphere by w(z) = (tan (1/4 (p- 2f)) ei l)^1/3, in which w(z) is the elliptical function defined by z = ∫ (1 - w ³)^-2/3 dw. The map projection was used by J. S. Cahill for one version of his butterfly map. It is related to ë and ö on the hemisphere by u(z) = w ²(z), where u(z) is substituted for w(z) in the integral defining z. The poles will be at the apices of the 120° angles.