I've said it before, but it bears repeating . . .
I've read three books about symmetry and two-dimensional patterns: one written by a mathemetician; the other two written by quilters.
All three books described the four operations of symmetry: translation, rotation, reflection, and glide reflection. All three books generated patterns using a method developed by crystallographers (even though crystallographers are not necessarily quilters, and vice versa). All three books overlooked two simple observations: all the patterns generated could be simplified to two pairs of squares beside each other, on top of each other, or diagonally from each other; and, in all but one instance, the squares were right side up or upside down, but never sideways.
I have previously described the operations of symmetry, but I will not generate any patterns with a method I now view as flawed. I propose a new symmetry which does not rely on any operations other than "pick a pair." I have presented the two tiles below to nearly 300 people. You've had a week or so to play with them.
Will you join me on a guided journey with these tiles??
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