Electrostatic interactions, base-pairing, and especially base-stacking dominate RNA three-dimensional structures. In an A-form RNA helix, base-stacking results in nearly perfect parallel orientations of all bases in the helix. Interestingly, when an RNA structure containing multiple helices is visualized at the atomic level, it is often possible to find an orientation such that only the edges of most bases are visible. This suggests that a general aspect of higher level RNA structure is a coplanar arrangement of base-normal vectors. We have analyzed all solved RNA crystal structures to determine the degree to which RNA base-normal vectors are globally coplanar. Using a statistical test based on the Watson-Girdle distribution, we determined that 330 out of 331 known RNA structures show statistically significant (p < 0.05; false discovery rate [FDR] = 0.05) coplanar normal vector orientations. Not surprisingly, 94% of the helices in RNA show bipolar arrangements of their base-normal vectors (p < 0.05). This allows us to compute a mean axis for each helix and compare their orientations within an RNA structure. This analysis revealed that 62% (208/331) of the RNA structures exhibit statistically significant coaxial packing of helices (p < 0.05, FDR = 0.08). Further analysis reveals that the bases in hairpin loops and junctions are also generally planar. This work demonstrates coplanar base orientation and coaxial helix packing as an emergent behavior of RNA structure and may be useful as a structural modeling constraint.