Given a d-polytope $P$ we define the c-dual polytope as $P^\ast = \{y\in R^d \mid x\cdot y\geq -c, \forall x\in P\}$. Then I say that a polytope is c-polar self-dual if $P=P^\ast$. I cannot find this definition of self-dual used in any research level publications and before I publish I would like to know who I need to cite. The only other place I have seen this discussed is in this question:
Does there always exist a self dual polytope that contains a given polytope contained in its dual?