VC dimension of the class of convex polygons with $ k $ vertices is known to be $ 2k + 1$.
For the general case I was able to derive a bound of the type $ O(k^2log(k)) $ (probably can be easily improved to O(klog(k)), this is not the issue). However, I found some hits (e.g. https://cs.nyu.edu/~mohri/ml/ml08/sol2.pdf) that VC dimension for this case is in fact also $2k + 1$. Any idea if this is correct?