The Santaló point 
of a convex body 
is the unique point 
in its interior
minimizing the volume of the polar
body 
. For a centrosymmetric
set that is a convex body, it is the center of
symmetry. For a simplex, it is the geometric
centroid.
Centering at 
defines the volume product 
used in the Mahler
volume product conjecture. The two volume factors
transform inversely under an invertible affine
transformation, so 
is affine invariant.
