M, N, O, P, Q, R, S and T are the values of the respective sums of the three vertices which form the respective surfaces to which each is assigned.

M + N = O + P = Q + R = S + T

Find

__unique sets of values__

^{1}for A, B, C, D, E and F such that the values of M through T (but not necessarily in that order) form series which increment by 2 of which there are 7.

Background statistics: Unique Actual M+N= Interval Sets^{2}Solutions 21 1 1 96 23 1 2 96 25 1 2 9626 296 27 1 5 480 29 1 4 288230 2144 31 1 8 288 33 1 6 480334 296 35 1 2 96 37 1 2 96 39 1219640 2448Note:^{1.}For M+N=21, 1, 2, 3, 6, 4, 5 1, 2, 3, 6, 5, 4 and 1, 2, 5, 3, 4, 6 are the first 3 of 96 solutions. The 96 values do not discriminate amongst vertex rotation or reflections.^{2.}Each unique set configures the octahedron in more ways than one.