A proportional model of Chicago's Sears Tower can be created from five Soma sets. The lower part of the tower is three complete Soma cubes, and the upper part can be created from two more Soma sets (with a couple of pieces left over).
Self-Supporting Cube 1
There are some 2288 solutions for the arrangement of cubelets in the Self-Supporting Cube 1 design (many of these are duplications due to symmetry), but only 40 avoid unsupported pieces in the next-to-lowest layer. All of the feasible solutions are permutations of an arrangement with a horizontal L and a Y or V in the top layer, a T along a vertical edge of the cube, and a base stub using a 3 or 9 piece. Unfortunately, none of these solutions provide a weight distribution that prevents the cube from falling apart laterally. While there are many ways to construct the cubelet arrangement in the absence of gravity, a truly self-supporting solution is impossible.
If the full Soma cube is to be supported on an external pedestal (such as the L piece from another Soma set), a valid solution can be obtained.
Self-Supporting Cube 2
There is no solution to this arrangement of cubelets, even if the self-supporting requirement is removed.
The Y Piece in the Basic 3 x 3 Cube
There are many solutions to the basic 3 x 3 cube design, but none in which the Y piece is imbedded in the center of the cube, with only its "arms" showing as the center squares on three of the the cube's faces. However, a solution exists in which the Y piece is not in a corner of the cube.
No solution exists to the one-set skyscraper design with the mast in the back, even though this design is shown in paperwork accompanying some modern Soma puzzles! Solutions exist for designs with the mast in any of the other three corners.
Solutions exist for short and tall 2-set versions of this design. Rearranging or swapping L and V pieces in the top layer of the short version allows the mast to be located in most other locations. A design with the mast in front or in the middle can be solved by a somewhat different arrangement of the pieces. Plane separations above and below the cube of 3 pieces in the tall version allow the mast to be rotated into any of the four corners.
We've added many new designs to the Soma Gallery, including two gondolas (one with a hidden cavity), a pyramid with a removable "roof", a pillbox, a hollow cube, two large snakes and a couple of turrets.
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