A FINITE BASIS THEOREM REVISITED : , l . BY DAVID A . KLARNER STAN - CS - 73 - 338 FEBRUARY 1973 COMPUTER SCIENCE DEPARTMENT School of Humanities and Sciences STANFORD UNIVERSITY

Let S denote a set of k-dimensional boxes each having integral sides. Let I'(S) denote the set or all boxes which can be filled completely with translates of elements of S . It is shown here that S contains a finite subset B such that l?(B) = I'(S) . This result was proved for k = 1,2 in an earlier paper, but the proof for k > 2 contained an error. This research was supported in part by the National Science Foundation under grant number GJ-992, and the Office of Naval Research under contract number N-00014-67-A-0112-0057 NR 044-402. Reproduction in whole or in part is permitted for any purpose of the United States Government.