A Hanner polytope is a convex polytope obtained recursively from centered line segments by taking
Cartesian products and the following convex
sums. If 
and 
are Hanner polytopes, their convex sum is the convex hull
of 
in 
.
Cartesian powers of centered line segments and cross polytopes are examples.
Every 
-dimensional
Hanner polytope 
has volume product
 |
where 
is its polar body. These are the proposed equality
cases in the symmetric Mahler volume
product conjecture.
