Reading clockwise from the top corner ~ one of the answers is ~ repeating the corners ~ 3-2-5,5-4-1,1-6-3
Another solution is ~ 4-5-2,2-3-6,6-1-4.
You will note that one of these answers totals 10, the other 11. The corner items play an important part in determining whether the total for the lines is smaller or larger, since they are each counted twice in the summations.
This suggests to me that there might be an even smaller ~ or an even larger ~ answer with a more judious choice of corner values. Maybe you would try finding them? ~ I would not suggest it if it was not possible. Go to it!
Further commentary ~ for subscribers only ~ is at [122121].