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What’s the maximum amount of unit cubes that can touch faces (not edges) with a central unit cube? I think this question is related to asking the max amount of cubes that can overlap with another cube.

How many unit squares can overlap a given unit square without overlapping each other?

I found this for 2D but I don’t know about 3D. I found an arrangement with 22 but can’t seem to get higher; I got an upper bound of 26 but I can’t seem to find an arrangement with 26 that has face-contact(not edges or vertices touching)

  • I don't see how the touching-faces question is equivalent to the overlapping question. It is certainly related to the overlapping squares question in the other post, which provides your 22 cube solution (8 each on 2 opposite faces per the answer to that quesiton, 2 cubes each on another pair of opposite faces, and 1 cube each on the final pair of faces), – Paul Sinclair Jul 24 '22 at 14:20
  • Nevermind, I fixed it –  Jul 26 '22 at 01:22

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