If we start by labelling the positions with letter A - L, as shown, then we can look at some of the relationships that must hold for the star to be correct. For example, in triangle ABC, the three lines each add to 26 and A, B and C are repeated. Thus:

2(A + B + C) + (G + ... + L) = 78

where we have separated out the inner hexagon formed by G to L.

A very similar equation holds for triangle DEF. Thus:

A + B + C = D + E + F

(more to follow soon!)