Vertices of some of polytopes generalized from the regular hexagon.
Main page.

G1:

± [[+1,−1]] ⇔ ± [2k0]

G2:

± [[+1,−1,0]] ⇔ ± [2k0,0]
± [[+1,0,−1]] ⇔ ± [k0,3k1]
± [[0,+1,−1]] ⇔ ± [−k0,k1]

G3:

± [[+1,−1,0,0]] ⇔ ± [2k0,0,0]
± [[+1,0,−1,0]] ⇔ ± [k0,3k1,0]
± [[0,+1,−1,0]] ⇔ ± [−k0,3k1,0]
± [[+1,0,0,−1]] ⇔ ± [k0,k1,4k2]
± [[0,+1,0,−1]] ⇔ ± [−k0,k1,4k2]
± [[0,0,+1,−1]] ⇔ ± [0,−2k1,4k2]

G4:

± [[+1,−1,0,0,0]] ⇔ ± [2k0,0,0,0]
± [[+1,0,−1,0,0]] ⇔ ± [k0,3k1,0,0]
± [[0,+1,−1,0,0]] ⇔ ± [−k0,3k1,0,0]
± [[+1,0,0,−1,0]] ⇔ ± [k0,k1,4k2,0]
± [[0,+1,0,−1,0]] ⇔ ± [−k0,k1,4k2,0]
± [[0,0,+1,−1,0]] ⇔ ± [0,−2k1,4k2,0]
± [[+1,0,0,0,−1]] ⇔ ± [k0,k1,k2,5k3]
± [[0,+1,0,0,−1]] ⇔ ± [−k0,k1,k2,5k3]
± [[0,0,+1,0,−1]] ⇔ ± [0,−2k1,k2,5k3]
± [[0,0,0,+1,−1]] ⇔ ± [0,0,−3k2,5k3]

G5:

± [[+1,−1,0,0,0,0]] ⇔ ± [2k0,0,0,0,0]
± [[+1,0,−1,0,0,0]] ⇔ ± [k0,3k1,0,0,0]
± [[0,+1,−1,0,0,0]] ⇔ ± [−k0,3k1,0,0,0]
± [[+1,0,0,−1,0,0]] ⇔ ± [k0,k1,4k2,0,0]
± [[0,+1,0,−1,0,0]] ⇔ ± [−k0,k1,4k2,0,0]
± [[0,0,+1,−1,0,0]] ⇔ ± [0,−2k1,4k2,0,0]
± [[+1,0,0,0,−1,0]] ⇔ ± [k0,k1,k2,5k3,0]
± [[0,+1,0,0,−1,0]] ⇔ ± [−k0,k1,k2,5k3,0]
± [[0,0,+1,0,−1,0]] ⇔ ± [0,−2k1,k2,5k3,0]
± [[0,0,0,+1,−1,0]] ⇔ ± [0,0,−3k2,5k3,0]
± [[+1,0,0,0,0,−1]] ⇔ ± [k0,k1,k2,k3,6k4]
± [[0,+1,0,0,0,−1]] ⇔ ± [−k0,k1,k2,k3,6k4]
± [[0,0,+1,0,0,−1]] ⇔ ± [0,−2k1,k2,k3,6k4]
± [[0,0,0,+1,0,−1]] ⇔ ± [0,0,−3k2,k3,6k4]
± [[0,0,0,0,+1,−1]] ⇔ ± [0,0,0,−4k3,6k4]

G6:

± [[+1,−1,0,0,0,0,0]] ⇔ ± [2k0,0,0,0,0,0]
± [[+1,0,−1,0,0,0,0]] ⇔ ± [k0,3k1,0,0,0,0]
± [[0,+1,−1,0,0,0,0]] ⇔ ± [−k0,3k1,0,0,0,0]
± [[+1,0,0,−1,0,0,0]] ⇔ ± [k0,k1,4k2,0,0,0]
± [[0,+1,0,−1,0,0,0]] ⇔ ± [−k0,k1,4k2,0,0,0]
± [[0,0,+1,−1,0,0,0]] ⇔ ± [0,−2k1,4k2,0,0,0]
± [[+1,0,0,0,−1,0,0]] ⇔ ± [k0,k1,k2,5k3,0,0]
± [[0,+1,0,0,−1,0,0]] ⇔ ± [−k0,k1,k2,5k3,0,0]
± [[0,0,+1,0,−1,0,0]] ⇔ ± [0,−2k1,k2,5k3,0,0]
± [[0,0,0,+1,−1,0,0]] ⇔ ± [0,0,−3k2,5k3,0,0]
± [[+1,0,0,0,0,−1,0]] ⇔ ± [k0,k1,k2,k3,6k4,0]
± [[0,+1,0,0,0,−1,0]] ⇔ ± [−k0,k1,k2,k3,6k4,0]
± [[0,0,+1,0,0,−1,0]] ⇔ ± [0,−2k1,k2,k3,6k4,0]
± [[0,0,0,+1,0,−1,0]] ⇔ ± [0,0,−3k2,k3,6k4,0]
± [[0,0,0,0,+1,−1,0]] ⇔ ± [0,0,0,−4k3,6k4,0]
± [[+1,0,0,0,0,0,−1]] ⇔ ± [k0,k1,k2,k3,k4,7k5]
± [[0,+1,0,0,0,0,−1]] ⇔ ± [−k0,k1,k2,k3,k4,7k5]
± [[0,0,+1,0,0,0,−1]] ⇔ ± [0,−2k1,k2,k3,k4,7k5]
± [[0,0,0,+1,0,0,−1]] ⇔ ± [0,0,−3k2,k3,k4,7k5]
± [[0,0,0,0,+1,0,−1]] ⇔ ± [0,0,0,−4k3,k4,7k5]
± [[0,0,0,0,0,+1,−1]] ⇔ ± [0,0,0,0,−5k4,7k5]

G7:

± [[+1,−1,0,0,0,0,0,0]] ⇔ ± [2k0,0,0,0,0,0,0]
± [[+1,0,−1,0,0,0,0,0]] ⇔ ± [k0,3k1,0,0,0,0,0]
± [[0,+1,−1,0,0,0,0,0]] ⇔ ± [−k0,3k1,0,0,0,0,0]
± [[+1,0,0,−1,0,0,0,0]] ⇔ ± [k0,k1,4k2,0,0,0,0]
± [[0,+1,0,−1,0,0,0,0]] ⇔ ± [−k0,k1,4k2,0,0,0,0]
± [[0,0,+1,−1,0,0,0,0]] ⇔ ± [0,−2k1,4k2,0,0,0,0]
± [[+1,0,0,0,−1,0,0,0]] ⇔ ± [k0,k1,k2,5k3,0,0,0]
± [[0,+1,0,0,−1,0,0,0]] ⇔ ± [−k0,k1,k2,5k3,0,0,0]
± [[0,0,+1,0,−1,0,0,0]] ⇔ ± [0,−2k1,k2,5k3,0,0,0]
± [[0,0,0,+1,−1,0,0,0]] ⇔ ± [0,0,−3k2,5k3,0,0,0]
± [[+1,0,0,0,0,−1,0,0]] ⇔ ± [k0,k1,k2,k3,6k4,0,0]
± [[0,+1,0,0,0,−1,0,0]] ⇔ ± [−k0,k1,k2,k3,6k4,0,0]
± [[0,0,+1,0,0,−1,0,0]] ⇔ ± [0,−2k1,k2,k3,6k4,0,0]
± [[0,0,0,+1,0,−1,0,0]] ⇔ ± [0,0,−3k2,k3,6k4,0,0]
± [[0,0,0,0,+1,−1,0,0]] ⇔ ± [0,0,0,−4k3,6k4,0,0]
± [[+1,0,0,0,0,0,−1,0]] ⇔ ± [k0,k1,k2,k3,k4,7k5,0]
± [[0,+1,0,0,0,0,−1,0]] ⇔ ± [−k0,k1,k2,k3,k4,7k5,0]
± [[0,0,+1,0,0,0,−1,0]] ⇔ ± [0,−2k1,k2,k3,k4,7k5,0]
± [[0,0,0,+1,0,0,−1,0]] ⇔ ± [0,0,−3k2,k3,k4,7k5,0]
± [[0,0,0,0,+1,0,−1,0]] ⇔ ± [0,0,0,−4k3,k4,7k5,0]
± [[0,0,0,0,0,+1,−1,0]] ⇔ ± [0,0,0,0,−5k4,7k5,0]
± [[+1,0,0,0,0,0,0,−1]] ⇔ ± [k0,k1,k2,k3,k4,k5,8k6]
± [[0,+1,0,0,0,0,0,−1]] ⇔ ± [−k0,k1,k2,k3,k4,k5,8k6]
± [[0,0,+1,0,0,0,0,−1]] ⇔ ± [0,−2k1,k2,k3,k4,k5,8k6]
± [[0,0,0,+1,0,0,0,−1]] ⇔ ± [0,0,−3k2,k3,k4,k5,8k6]
± [[0,0,0,0,+1,0,0,−1]] ⇔ ± [0,0,0,−4k3,k4,k5,8k6]
± [[0,0,0,0,0,+1,0,−1]] ⇔ ± [0,0,0,0,−5k4,k5,8k6]
± [[0,0,0,0,0,0,+1,−1]] ⇔ ± [0,0,0,0,0,−6k5,8k6]