this post was submitted on 09 May 2026
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Wait, isn’t this trivial?
If we’re talking about “faces” as in the cubic faces of a tesseract then each of the 8 faces are connected to all other faces except the opposite face. So just spiral around from your starting face (keeping the faces you’ve visited on the inside of the spiral) and you’re fine.
If you mean 2D faces connecting the 3D ones, then things get more difficult but not that much because you can do the exact same thing. Choose a 1D edge as your origin, pick a face touching that edge to start with, traverse that edge twice to get the next two faces. Then traverse three faces which share edges with those faces you already traversed (there are 6 faces with this property, 3 for each vertex of our origin edge, the set you pick determines the “direction” of your overall progress through/around the tesseract). Repeat that step again but for the faces that share edges with two of the three you just did. Repeat again and again and again until the last three faces share a vertex with the origin edge you started with. You’re done.
Am I missing something? Did the prompt mean to say you can only traverse each edge once?
Edit: the 2D face path I described would miss 6 faces. Those six faces should be traversed in the middle, so do the first three faces, the second three, then all six which touch those last three and the three you would have done next on the original path. Then do the rest just like I originally mentioned.
I understood some of those words.
Have you ever seen one of those images of a tesseract where it’s like a cube in a cube? (You can just look up “tesseract” to find an image)
Now, pick one of the corners of the outer cube and find the line that connects it to a corner of the inner cube. That’s our origin “edge” and we’re basically just going to move in through the cube along that direction.
There are three “faces” which share that “edge” (line). We do those ones first.
Then we move deeper in and do the three faces of the inner cube which share the corner our origin line connects to.
Then we have to zig zag around the six “faces” that exist between inner and outer cubes which are roughly perpendicular to our origin edge. (Imagine you broke the tesseract in half by cutting halfway between your starting corner and the corner opposite it. The “faces” we need to traverse would intersect that plane)
After that, we do the three faces on the far side of the inner cube. (The ones opposite our starting corner)
Then we do the three around the line which connects that far corner of the inner cube to the outer cube.
Then we do the three faces on the outside of the large cube at that corner.
Finally we do the three faces on the outside of the cube around our starting corner.
But the sentences continue to elude me