Fitting a simplex symmetrically

Abstract
A method for fitting a perfect simplex [Guttman, 1954] is suggested which, in contrast to Kaiser's [1962], is independent of the order of the manifest variables. It is based on a procedure for scaling a set of points from their pairwise distances [Torgerson, 1958; Young & Householder, 1938] which is reviewed in compact notation in the Appendix. The method is extended to an iterative algorithm for fitting a quasi-simplex. Some empirical results are included.