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Here are some examples of transcendental solutions in various categories. By the nature of transcendency, the beam pattern can be removed without any loss of information.

2 groups, diagonal symmetry

2 groups, diagonal symmetry

The eight diagonally symmetric pieces are in the axis of this two groups solution.

Note that the number of groups equals the number of loops.

Here's an inlaid picture of the above solution that I made in May 1987.

compact art