12 Bar Puzzle

I designed this puzzle from scratch, although I guess it could exist elsewhere. The aim of the puzzle is to insert all 12 bars in to the cube such that they protrude equally on all sides, as shown in the image. I printed this in Bambu Lab PLA Silk+, although other filaments should work too. Initially any piece should slid through any hole, and it's probably worth sliding them though a few times to make sure everything works smoothly once printed. Solving the puzzle (SPOILER ALERT!): This isn't a complete step by step solution, but it does explain the logical thought process behind solving it. There are 12 bars, and each bar partially intersects with four other bars, and the bars have various cutouts to allow other bars to slide past them, once inserted. As with all similar puzzles, the last part to insert has no cutouts, and it follows that the first piece to insert must have four cutouts, as four other bars must slide past it. As there is only one bar with four cutouts, it als