There is a geometric enigma in LOCKED SQUARES which does not show itself until you begin to select the colors for the block. And then you realize that it requires exactly 5 different hues for the stars, no more, no less. That's because each of the pointed wings borders each of the others at the tip and would therefore merge if the same colors were repeated. The background is ordinarily white or a light shade, the illustration upper left is obviously a variation. It is a devilish thing to figure out the repeat for this design. Nancy Cobot's suggested off-centered solution, published in her Chicago Tribune column on October 21, 1937, though seeming a bit awkward as a single block, actually works quite well as a continuous pattern (see the tessellation below). Cabot comments:
"LOCKED SQUARES is one of those enigmatic quilt patterns which cause all women to exclaim, 'How unusual.'"
And a perfectly named design too. The idea of "locking" is expressed in the "hand-holding" of each of the pointed squares in all four directions. Note: the light tangerine background fill illustrated upper right was created with a compressed version of a fractal, called a "Z-order curve," illustrated at Wikipedia.
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SQUARES UPON SQUARES