The average and local structures of -22 nm β-Er:Yb:NaYF4 upconverting nanocrystals were probed using a dual-space approach combining Rietveld and pair distribution function analysis of X-ray total scattering. Comparison of the fits provided by the structural models derived from P6¯2m, P6¯, and P63/m space groups demonstrates that the latter yields a crystallochemically meaningful description of the nanocrystals' average and local structures. This result is in line with those previously reported for bulk β-Na3xRE2-xF6 (x - 0.45; RE = Y, Er, Tm, Yb) using powder X-ray diffraction, 1 and for β-NaREF4 (RE = Y, Lu) nanocrystals using solid-state NMR;2 however, it differs from those reported in studies of β-NaREF4 (RE = La, Gd, Er) single crystals, which favored the structural model derived from the P6¯ space group.3 The proposed structural model features sodium cations distributed in four translation-equivalent chains, each shifted relative to the others along the c axis. Interestingly, the structural model derived for the mineral gagarinite (NaCaREF6, P63/m), in which sodium cations are distributed in eight chains, also provides an adequate fit to the X-ray scattering data. The potential implications of this finding are discussed from the perspective of the size dependence of the crystal structure of β-NaREF4. [ABSTRACT FROM AUTHOR]