Frénicle standard form

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A magic square is in Frénicle standard form, named for Bernard Frénicle de Bessy, if the following two conditions apply:

1. the element at position [1,1] (top left corner) is the smallest of the four corner elements; and
2. the element at position [1,2] (top edge, second from left) is smaller than the element in [2,1].

This standard form was devised since a magic square remains "essentially similar" if it is rotated or transposed, or flipped so that the order of rows is reversed — there exists 8 different magic squares sharing one standard form. For example, the following magic squares are all essentially similar, with only the final square being in Frénicle standard form:

 8 1 6   8 3 4     4 9 2   4 3 8     6 7 2   6 1 8     2 9 4   2 7 6
 3 5 7   1 5 9     3 5 7   9 5 1     1 5 9   7 5 3     7 5 3   9 5 1
 4 9 2   6 7 2     8 1 6   2 7 6     8 3 4   2 9 4     6 1 8   4 3 8