A minimal informationally complete measurement is s-tight if and only if its suitably rescaled vectors form an acute orthocentric simplex centered at the origin, equivalent to homothetic self-duality.
de Longchamps, Sur le t´ etra` edre orthocentrique, Mathesis 10 (1890), 49–53, 77–82
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From minimal informationally complete measurements to orthocentric simplices and back again
A minimal informationally complete measurement is s-tight if and only if its suitably rescaled vectors form an acute orthocentric simplex centered at the origin, equivalent to homothetic self-duality.