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
A α / \ ζ B---C---D---E β \ / \ / F G / \ / \ ε H---I---J---K γ \ / L δAssign 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.
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?
Discounting rotations and reflections, more than one possibility exists for each of the first two tasks.