The extreme projections of the regular simplex

Filliman, P.

doi:10.1090/S0002-9947-1990-0989573-6

The extreme projections of the regular simplex
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Trans. Amer. Math. Soc. 317 (1990), 611-629 Request permission

Abstract:

The largest and smallest projections of the regular $n$-dimensional simplex into a $k$-dimensional subspace are determined for certain values of $n$ and $k$. These results suggest that the smallest $k$-dimensional projection and the largest $(n - k)$-dimensional projection occur in orthogonal subspaces of ${R^n}$.

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