The single-crystal structure of |$Ca_{35.5}$|[$Si_{121}Al_{71}O_{384}$]-FAU, $Ca_{35.5}Si_{121}Al_{71}O_{384}$ per unit cell, a = 24.9020(10) $AA$, dehydrated at 673 K and 2 ${ imes};10^{-6}$Torr, has been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd$overline{3}$m at 294 K. The large single crystals of zeolite Y (Si/Al = 1.70) were synthesized up to diameters of ${mu}m;and;Ca^{2+}$-exchanged zeolite Y were prepared by ion exchange in a batch method of 0.05 M aqueous Ca($NO_3)_2$ for 4 hrs at 294 K. The structure was refined using all intensities to the final error indices (using only the 971 reflections for which $F_o;>;4{sigma}(F_o));R_1$ = 0.038 (based on F) and $R_2$ = 0.172 (based on $F^2$). About 35.5 $Ca^{2+}$ ions per unit cell are found at an unusually large number of crystallographically distinct positions, four. Nearly filling site I (at the centers of the double 6-rings), 14.5 octahedrally coordinated $Ca^{2+}$ ions (Ca-O = 2.4194(24) $AA$ and O-Ca-O = 87.00(8) and 93.00($8^o$) are found per unit cell. One $Ca^{2+}$ ion per unit cell is located at site II’ in the sodalite cavity and extends 0.50 $AA$ into the sodalite cavity from its 3-oxygen plane (Ca-O = 2.324(13) $AA$ and O-Ca-O = 115.5(10)o). The remaining twenty $Ca^{2+}$ ions are found at two nonequivalent sites II (in the supercages) with occupancies of 10 and 10 ions, respectively. Each of these $Ca^{2+}$ ions coordinates to three framework oxygens, either at 2.283(3) or 2.333(5) $AA$, respectively, and extends either 0.24 or 0.54 $AA$, respectively, into the supercage from the three oxygens to which it is bound. In this crystal, site I is the most populated; sites II’ and II are only sparsely occupied.$Ca^{2+}$+ appears to fit the octahedral site I best. No cations are found at sites III or III’, which are clearly less favorable for $Ca^{2+}$ ions in dehydrated zeolite Y.