The SOMA Cube 

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• How many unique solutions does the SOMA Cube have (excluding rotations/reflections)?

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• What defines a solution as truly "unique"?

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• How can you prove that two configurations are not the same under rotation or reflection?

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• What mathematical or algorithmic methods could be used to count all unique solutions?

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• Which faces of the final cube are always exposed? Are there parts that are never exposed?

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• Can any piece never occupy a corner of the cube? Why or why not?

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• Is it possible for a piece to be completely surrounded—fully internal—in any solution? If so, which one(s)?

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• Could the same piece always end up in the center of the cube across all unique solutions? How would you check?

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• Can the SOMA Cube concept be extended to build a 4×4×4 cube? What new rules or patterns would be needed?

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• What other 3D shapes can you build using all 7 Soma pieces?

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• Could a Soma-like puzzle be built to form a different solid (like a tetrahedron)?

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• What new question did this activity spark for you?

   

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