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  "body": "\n## Summary\n\nIn mathematics, a **duality** translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a [[one-to-one|09NWETVTNY]] fashion, often (but not always) by means of an involution operation: if the dual of $A$ is $B$, then the dual of $B$ is $A$. In other cases the dual of the dual – the double dual or bidual – is not necessarily identical to the original (also called *primal*). Such involutions sometimes have fixed points, so that the dual of $A$ is $A$ itself. For example, Desargues' theorem is **self-dual** in this sense under the *standard duality in projective geometry*.\n",
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