Tesseract and 16-cell faces

This list shows the $$3^4 = 81$$ of the  and its dual.

The sign vectors (with entries 1, 0, −1) in the following table are the face centers of the tesseract. (Compare .) The indices on the left (between −40 and 40) are their interpretation as little- numbers. The columns to their right are their sums, patterns of non-zero entries, and Hamming weights (numbers of non-zero entries). The default order of the table is first by Hamming weights, then by patterns, and then by sums.