The largest projections of regular polytopes (Q1117463)

The author studies the problem of finding the projections of the regular n-dimensional simplex and crosspolytope into \({\mathbb{R}}^ k\) with the largest k-volume. [For the cube, see a paper by \textit{G. D. Chakerian} and the author, Stud. Sci. Math. Hung. 21, 103-110 (1986; Zbl 0621.52001)]. Explicit solutions are found for the cases \(k=2\), \(n\geq 2\) and \(k=3\), \(4\leq n\leq 6.\) For the other cases, upper bounds are established. The proofs rely on a former paper by the author [``Projections of polytopes'', to appear in Discrete Comput. Geom.] and involve exterior algebra and computer gradient methods.