Tesseract Gauntlet

The grid is ℤ₃⁴ — miss a key and the hypercube turns on you

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Six constraint families — hover to trace one on the board
Amber cells share a classic group with your selection; teal cells share a four-dimensional one.
The same 81 cells at their true positions in the lattice. Drag to turn it in 3-space; shift-drag (or 4D drag) to turn it through w and watch it fold inside out. Click any digit to select it — its six constraint planes render in place.