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This page shows solutions with 93.3% horizontal symmetry.
In each solution, just FOUR segments are asymmetric.

In this figure, the symmetry is better shown.
Note how the two outside columns can be permuted to generate 300 solutions, all with the same center three columns.
See corners5.html for solutions with 93.3% diagonal symmetry.

Solids position Most symmetric solutions Total solutions
A fourth symmetric position of solids (2,11,13), has 6552 solutions, with 32 of them having maximum symmetry of 88%, slightly below the ones shown here.
  Red is symmetric with itself, and blue with green.