The structure of a single crystal of fully dehydrated K+-exchanged zeolite X was determined by X-ray diffraction methods in the cubic space group Fd (3) over bar m at 21 degrees C; a(o) = 25.083(5) Angstrom. Ion-exchange of a crystal of Na92Si100Al92O384 was done at 80 degrees C using flowing aqueous 0.1 M KNO3 with pH = 12; 90(3) K+ ions were found per unit cell. R-1 = 0.066 for 352 reflections for which F-o > 4 sigma(F-o); wR(2) based on F-2 and all data is 0.193. The structure of dehydrated K-X is much more complex than that of dehydrated Na-X; K+ ions are found at nine crystallographic sites, a large number due to cation crowding. Two distinct site I and three site I' positions are occupied by six, eight, four, four, and four K+ ions per unit cell, respectively. Ten of the 16 double six-rings each accommodate two K+ ions with short K+... K+ distances of 3.79(4) and 3.92(8) Angstrom, indicative of the degree of cation crowding. Site II is nearly fully occupied with 28.4(4) K+ ions. The remaining 36 K+ ions are found at one III and two III' sites; these appear to be close in energy for K+ ions so that no single site is preferred.