Show that for $n\ge 5$, a cross-section of a pyramid whose base is a regular $n$-gon cannot be a regular $(n + 1)$-gon. This is a conjecture I came across while trying to solve this problem. I was drawing many figures and three dimensional figures and pyramids were the first choice. And I observed this. I have no proof, or even ideas to a proof. But seems true. Any counter example would be nice. Thanks.