To get Figure 1 in the article "Maximally Nontransitive dice" by Joe Buhler, Ron Graham, and Al Hales http://www.math.ucsd.edu/~ronspubs/pre_nontransitive.pdf Note , in the rightmost tournament the arrow from C to B should be from B to C is [[[[0, 1, -1], [-1, 0, 1], [1, -1, 0]], {1, 4}], [[[0, -1, 1], [1, 0, -1], [-1, 1, 0]], {2, 5, 8}], [[[0, 1, 1], [-1, 0, 1], [-1, -1, 0]], {3, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}]] To prove the claim in Remark 5 on p. 398. [[[[0, 1, 1], [-1, 0, 1], [-1, -1, 0]], {1, 5}], [[[0, 1, -1], [-1, 0, 1], [1, -1, 0]], {2}], [[[0, 1, -1], [-1, 0, -1], [1, 1, 0]], {3}], [[[0, 1, 1], [-1, 0, -1], [-1, 1, 0]], {4}], [[[0, -1, -1], [1, 0, 1], [1, -1, 0]], {6}], [[[0, -1, 1], [1, 0, 1], [-1, -1, 0]], {7}], [[[0, -1, 1], [1, 0, -1], [-1, 1, 0]], {8}], [[[0, -1, -1], [1, 0, -1], [1, 1, 0]], {9}]]