"Impossible" being the operative word! I used a lot of guesswork, had an answer that satisfied the numbers, but it was invalid. Therefore, multiple solutions. Please test your puzzles before submitting them (when you click "save", there is the option of "try"). This is why on my ones I say "logical" and "tested" so that people know they are possible.
While the puzzle can be completed assuming it has a symmetrical frame, the accepted answer is actually the appearance of an impossible cube like the title suggests. Guesswork is still required as it has multiple solutions, but once the inside has been completed the real placement of the edges is easy to see.
Multiple possible solutions. When there are several single squares forming a diagonal line, these squares are often ambiguous, as you can switch the placement of the squares for alternative solutions. This is a very cool design though. Thank you for the puzzle.
Please test your puzzles before submitting them (when you click "save", there is the option of "try").
This is why on my ones I say "logical" and "tested" so that people know they are possible.
Most of the puzzle can be guessed after the two main diagonal lines are filled in.
R2 C6 to R6 C2 ; R15 C19 to R19 C15
Additional hints if needed: R13 C6 ; R15 C7.