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.
