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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?

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Judging by Google search results, self-dual cones were studied quite a bit. Since self-dual bodies in $R^d$ are precisely compact hyperplane sections of self-dual cones in $R^{d+1}$, it should be possible to translate many results from one context to the other. – Sergei Ivanov Dec 5 '13 at 20:23

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