The rearrangement cone is permutation-invariant::
sage: all( is_permutation_invariant(rearrangement_cone(p,n))
- ....: for n in xrange(3, 6)
- ....: for p in xrange(1, n) )
+ ....: for n in range(3, 6)
+ ....: for p in range(1, n) )
True
As is the nonnegative orthant::