Radial symmetry is essential for the conventional view of the polymer spherulite microstructure. Typically it is assumed that, in the course of the spherulite morphogenesis, the lamellar crystals grow radially. Using submicron X-ray diffraction, it is shown that in banded spherulites of poly(propylene adipate) the crystals have the shape of a helix with flat-on crystals winding around a virtual cylinder of about 6 mu m in diameter. The helix angle of 30 degrees implies that the crystal growth direction is tilted away from the spherulite radius by this angle. The implications of the helical crystal shape contradict the paradigm of the spherulitic microstructure. The radial growth rate of such spherulites does not correspond to the crystal growth rate, but to the propagation rate of the virtual cylinder the ribbons wind around.