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Matthew Thomason, Blotch 9.7.11, Pencil, paper, photoshop, 8"x8"

This diagram outlines two scenarios for a double-cube.  Figures 1a, 1b, 2a, and 2b are all double-squares.  Figures 1a and 1b both illustrate two distinct squares made from two distinct lines(where 1a's are overlapping and 1b's are concentric).  Figures 2a and 2b (which I do not differentiate), however, represent two squares that are made from one continuous line that crosses itself.

Rows 1 and 2 illustrate the construction of double-cubes made from the two different types of double squares.

A quick-google for 'double-square' yields the following two (among many) interesting finds for today.  Check 'em out.  Stay tuned!