Coral skeletons were long assumed to have a spherulitic structure, that is, a radial distribution of acicular aragonite (CaCO3) crystals with their c-axes radiating from series of points, termed centers of calcification (CoCs). This assumption was based on morphology alone, not on crystallography. Here we measure the orientation of crystals and nanocrystals and confirm that corals grow their skeletons in bundles of aragonite crystals, with their c-axes and long axes oriented radially and at an angle from the CoCs, thus precisely as expected for feather-like or "plumose" spherulites. Furthermore, we find that in both synthetic and coral aragonite spherulites at the nanoscale adjacent crystals have similar but not identical orientations, thus demonstrating by direct observation that even at nanoscale the mechanism of spherulite formation is non-crystallographic branching (NCB), as predicted by theory. Finally, synthetic aragonite spherulites and coral skeletons have similar angle spreads, and angular distances of adjacent crystals, further confirming that coral skeletons are spherulites. This is important because aragonite grows anisotropically, 10 times faster along the c-axis than along the a-axis direction, and spherulites fill space with crystals growing almost exclusively along the c-axis, thus they can fill space faster than any other aragonite growth geometry, and create isotropic materials from anisotropic crystals. Greater space filling rate and isotropic mechanical behavior are key to the skeleton's supporting function and therefore to its evolutionary success. In this sense, spherulitic growth is Nature's 3D printing.