Conjoined Somas is two sets of Soma Cube pieces, made from truncated octahedra. The red set forms one cube, and the green set another. The two sets fit through each other.
Whereas each set is simple to solve (240 solutions for a regular Soma Cube), the combination is much harder, as most fitting combinations cannot be disassembled. Rick Eason computed that there exists 11,105,280 assemblies, than that from those at most 2,457,278 can be assembled (i.e. about 1 in 4.5 puzzles.) Rick only checked at the piecewise level, whether each individual green piece from an assembly could be separated from each individual red one. So most likely there are even fewer assemblies that can be actually disassembled.
The set of pieces took 18½ hours to 3D print on a Dutchy 3D printer, plus lots of glue to connect all pieces ruggedly with metal pins. 60 meter of 1.75-mm PLA filament was used to print it. The puzzle weights 216 gram: 178 gram of PLA plastic and 38 gram of metal pins.
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