On Regular Polytopes of 2-Power Order.

For each d ≥ 3 , n ≥ 5 , and k 1 , k 2 , ... , k d - 1 ≥ 2 with k 1 + k 2 + ⋯ + k d - 1 ≤ n - 1 , we show how to construct a regular d-polytope whose automorphism group is of order 2 n and whose Schläfli type is { 2 k 1 , 2 k 2 , ... , 2 k d - 1 } . [ABSTRACT FROM AUTHOR]