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The walk is comprised of all 11 nets of the cube, overlapping only at pendant vertices. So the path is really a chain of pentominoes — there are 5×11=55 squares in the path. I wanted no excessive touching between the nets, meaning besides the overlapping at one square (necessitating those to be the pendant ones), I didn't want any edge adjacency between other squares of different nets. It took a while to find such a thing and I cannot claim the approach I took was very elegant. But it's cute enough for now. A similar thing can probably be done with the 11 nets of the octahedron. (How about the 43380 nets of the dodec or icos?)