MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.