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 ]