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The placement of squares and diamonds is half-and-half across the upper-right/lower-left diagonal.

The solids are placed symmtrically with respect to the first diagonal.
Three placements are shown: blue on the upper-left/lower-right diagonal, and red and green symmteric on either side of it.

 Solidpositions Symmetric solutions/Total solutions Degree ofsymmetry 0,2,10 5 / 84,007 77% 0,3,15 11 / 548,335 77% 6,8,16 2 / >750,000 88%

A second arrangement of diamonds and squares produces other results:
Solids at 0,9,21: 2 of 44 solutions have 77% symmetry.
Solids at 0,3,15: 2 of 42 solutions have 82% symmetry.

For this "stripe" configuration, several positions produced symmetry of 83.3% or more. Interestingly, a couple of them (marked with *'s) do NOT place the solids symmetrically! For more information, see corners3sum.html. For an exploration of the reverse pattern of diamonds and squares, see corners5.html. That configuration has solutions with even fewer segments asymmetric.

 Solidpositions Symmetric solutions/Total solutions Degree ofsymmetry 1,10,18* 2 / 11 83.3% 2,10,18 3 / 68 85% 6,13,17 32 / 7756 90% 2,11,17* 8 / 20194 83.3% 1,16,19 12 / 92 83.3%