I was wondering for a face, does it matter which of its halfedge we choose to have it point to?

@mapqh, I'd assume it doesn't matter because we can just traverse the face using halfedge->next to find any vertex/edge we want, but could someone else confirm?

Yup, I think so too. If we have an access to any of the face's halfedges, we can iterate using next().

here looks Vertex, Edge, Face all point to only 1 *hafedge pointer, the halfedge pointer will present the all the data structure it needed.