[math-fun] Parametrization of an octant of the sphube puzzle

By analogy with the squircle we define the sphube (pron.: sfyoob) as the surface Sphu given by Sphu = {(x, y, z) in R^3 | x^4 + y^4 + z^4 = 1}. Puzzle: Find a simple explicit parametrization of the first octant of the sphube: U = {(x, y, z) in [0, oo)^3 | x^4 + y^4 + z^4 = 1} by a continuous bijective map h : Q —> U from the square Q = [0, 1]^2 onto U. —Dan