Large colorless single crystals of sodium zeolite X, stoichiometry |Na80 |[Si112Al80O384]-FAU, with diameters up to 200 μm and Si/Al = 1.41 have been synthesized from gels with the composition of 2.40SiO2 : 2.00NaAlO2 : 7.52NaOH : 454H2O : 5.00TEA. One of these, a colorless octahedron about 200 μm in cross-section has been treated with aqueous 0.1 M KNO3 for the preparation of K+-exchanged zeolite X. The crystal structure of |K80|[Si112Al80O384]-FAU per unit cell, a = 24.838(4) A, dehydrated at 673 K and 1 × 10-6 Torr, has been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd at 294 K. The structure was refined using all intensities to the final error indices (using only the 707 reflections for which Fo > 4σ (Fo)) R1 = 0.075 (based on F) and R2 = 0.236 (based on F2). About 80 K+ ions per unit cell are found at an unusually large number of crystallographically distinct positions, eight. Eleven K+ ions are at the centers of double 6-rings (D6Rs, site I; K-O = 2.492(6) A and O-K-O (octahedral) = 88.45(22)o and 91.55(22)o). Site-I' position (in the sodalite cavities opposite D6Rs) is occupied by five K+ ions per unit cell; these K+ ions are recessed 1.92 A into the sodalite cavities from their 3-oxygen planes (K-O = 2.820(19) A, and O-K-O = 78.6(6)o). Twety-three K+ ions are found at three nonequivalent site II (in the supercage) with occupancies of 5, 9, and 9 ions; these K+ ions are recessed 0.43 A, 0.75 A, and 1.55 A, respectively, into the supercage from the three oxygens to which it is bound (K-O = 2.36(13) A, 2.45(13) A, and 2.710(13) A, O-K-O = 116.5(20)o, 110.1(17)o, and 90.4(6)o, respectively). The remaining sixteen, thirteen, and twelve K+ ions occupy three sites III' near triple 4-rings in the supercage (K-O = 2.64(3) A, 2.94(3) A, 2.73(5) A, 2.96(6) A, 3.06(4) A, and 3.08(3) A).