The crystal structure of MAg4I5(M = K, Rb, NH4) is cubic with a= 11.2 Å, z= 4 and space group of the enantiomorphic pair P4132 and P4332. The locations of the I– and M+ ions have been deduced from symmetry and packing considerations. The Ag+ ions do not occupy distinct single sites, but are distributed randomly over a number of interstitial positions. This model is consistent with the expectionally high mobility of the Ag+ ions and the high entropy of formation of the compound. The absence of Na or Cs analogues is explained by the steric requirements of the proposed structure.