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This page shows the 37 possible placements of the solids with squares in two corners and the rest diamonds.

These placements show up twice:
0,3,15 (Bottom / Right)
0,3,21 (Left / Right)
0,9,19 (Top / Bottom)
0,9,21 (Top / Left)
1,3,15 (Bottom / Right)
1,8,19 (Left / Bottom)