This page shows possible placements of the solids with
the diamonds and squares making an hourglass formation.
There are just 630 solutions.
The first two sections have the pattern rotated 90 degrees,
so the squares are at the sides. The four solutions dubbed
"Most Symmetric" have just 4 segments out of symmetry:
right and left of the center, and two others on the right
and left borders.
Several solutions feature Rings, Rabbits, and Figure 8's.