This is a Light and Shadow with some special added rules:

  • Despite the visible puzzle grid being half a cube (in part due to penpa limitations), the grid for this puzzle is in fact a full six-sided cube; however, every single cell is connected via portal to its antipode (if the cube is centered around the origin, its antipode would have negative coordinates from the original cell).
  • A cell must be shaded if and only if its antipode/portaled cell is not; furthermore, all clues on the visible sides of the cube are reproduced with color inverted on their antipodes, consistent with the portal rule.

Those of you with topology knowledge might recognize this as being secretly based on the real projective plane. The puzzle was created for a Logic Showcase on the Puzzlers Club Discord server with a theme of portals; thanks to phenomist who ran it and had the detailed rules use the word “involution”, inspiring my puzzle idea. While it ended up on the bottom half of the entries that were submitted in terms of votes, it did recieve many notlikeduck reactions (Psyduck with his signature headache) when it was posted, which is a win of its own kind.