struct half_edge;

struct vertex {
    struct half_edge *rep;  /* rep->tail == this */
};

struct face {
    struct half_edge *rep;  /* rep->left == this */
};

struct half_edge {
    struct half_edge *prev;  /* prev->next == this */
    struct half_edge *next;  /* next->prev == this */
    struct half_edge *twin;  /* twin->twin == this */
    struct vertex *tail;     /* twin->next->tail == tail &&
                                prev->twin->tail == tail */
    struct face *left;       /* prev->left == left && next->left == left */
};