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—

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

This can be seen in the following regrouping—

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

Update of Feb. 5, 2011—