α = A + D + G + K β = E + G + J + L γ = K + J + I + H δ = L + I + F + B ε = H + F + C + A ζ = B + C + D + E

Assign values from 1 to 12 to each of the locations A to L such that each sum is an element of an arithmetic progression with an arithmetic difference of two (2) but not necessarily as adjacent vertex values.A α / \ ζ B---C---D---E β \ / \ / F G / \ / \ ε H---I---J---K γ \ / L δ

Secondly, attempt the same task but with a difference of four (4) as the outcome.

And for a tease... can you offer a solution if all such vertex sums are equal, ie, 26?

__Note:__Discounting rotations and reflections, more than one possibility exists for each of the first two tasks.