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The Order-4 Latin Squares

by Steven H. Cullinane, Jan. 22, 2011

The following is from the weblog of a high school mathematics teacher—

This is related to the structure of the figure on the cover of the 1976 monograph Diamond Theory

Each small square pattern on the cover is a Latin square,
with elements that are geometric figures rather than letters or numerals.
All order-four Latin squares are represented.

For a deeper look at the structure of such squares, let the high-school
chart above be labeled with the letters A through X, and apply the
four-color decomposition theorem.  The result is 24 structural diagrams—

    Click to enlarge

IMAGE- The Order-4 (4x4) Latin Squares

Some of the squares are structurally congruent under the group of 8 symmetries of the square.

This can be seen in the following regrouping—

   Click to enlarge

IMAGE- The Order-4 (4x4) Latin Squares, with Congruent Squares Adjacent

     (Image corrected on Jan. 25, 2011-- "seven" replaced "eight.")

Update of Feb. 5, 2011—

Click to enlarge
Latin Squares of Triangles