Catalogue of Asymmetric Closed Knight's Tours of the 6 by 6 Board

This page shows those with 4 and 12 slants.

Part 1: Tours with 4 Slants (total 60)

The angles occurring are b, e, g, i, l, n only. (There are a further 10 symmetric tours with 4 slants, consisting of 4 with quaternary symmetry ee/ee, gg/gg, ii/ii, ll/ll and 6 with binary symmetry bb/ii bb/nn, ee/gg, gg/ii, gg/nn, ii/ll, as shown in the 6×6 introduction.)

The tours are grouped in batches of 15 – since this number conveniently fits into a computer screen view area.

4 Slants, 60 tours, first 15: bb/in to bi/el.

4 Slants, 60 tours, second 15: bi/gi to ee/eg.

4 Slants, 60 tours, third 15: eg/eg to gg/in.

4 Slants, 60 tours, last 15: gi/gi to il/ll.

Part 6: Tours with 12 Slants (total 44)

(The total becomes 46 when the symmetric cases, quaternary aa/aa and binary cc/ff are included.)

The 12-slant tours are those whose four central angles are of the types a, c, f, m, each formed of 2 slants. In the 12-slant tours the consonant and vowel nets must be divided 2:4 or 3:3. The ac/ac is the only one with both divided 2:4. The 28 cases with one 2:4 and one 3:3 are those including an odd number (1 or 3) of 'c' angles. The other 17 cases have both divisions 3:3, including the symmetric aa/aa and cc/ff.

14 tours aa/aa to ac/ac.

15 tours, ac/af to ac/ff

15 tours, ac/fm to cf/ff

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