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Diagonal of Diamonds

This page shows possible placements of the solids with squares on two opposite 6-piece corners and the rest diamonds.
Solutions exist for 62 possible placements of the solids for squares in upper right/lower left, and for 83 possible placements of the solids for squares in upper left/lower right.

The numbers of solutions varies from 1 to 32102, quite a range!

Thirty-eight positions of solids show up for both directions:
0,2,4 0,2,9 0,2,10 0,2,11 0,2,13 0,2,14 0,2,15 0,2,20
0,2,22 0,3,11 0,3,13 0,3,14 0,3,22 0,4,11 0,4,17 0,4,22
0,4,7 0,7,9 0,9,17 0,9,22 1,3,10 1,3,11 1,3,22 1,9,10
1,9,22 1,10,14 1,10,19 1,10,21 1,10,22 1,10,23 1,11,22 1,11,23
1,13,22 1,14,21 1,14,22, 2,10,14 2,11,13 2,11,22

corners3sum.html has a complete summary of the number of solutions and symmetry for each position of the solids. corners5.html details solutions where the diamonds and squares are reversed.