Logic Masters Deutschland e.V.

I have a certain fascination with highly symmetric polytopes and remembered this when trying to think of some sort of theme for a puzzle. I am still quite new to setting and don't seem to have the patience to make a 9×9, so here is a proof-of-concept on a variant of Yin Yang I'm calling "Tetrahedron".

Click to play

• Normal sudoku rules apply: Place a number between 1 and 6 into each cell such that no digit repeats in a row, column or 2×3 box.
• Partial Kropki: White dots lie between consecutive digits. Not all dots are necessarily given.
• Tetrahedron: Divide the entire grid into four orthogonally connected regions, called faces of the tetrahedron. No 2×2 square in the grid may consist of cells from only one face. Each face must share at least one border with all other faces.
• Cages: Each cage entirely belongs to a single face of the tetrahedron, and contain digits that sum to the number in the top left corner if given. All cages appearing within a single face have sums that are congruent to each other modulo 4; that is, they share a remainder when divided by 4. This remainder is unique for each face; i.e. no two different faces contain cages that are congruent to each other modulo 4.

An example is provided below. I don't think that this is uniquely solvable but hopefully shows the key points!