A flat 2D grid keeps every cell adjacent to every input that's one bit away — which is the entire mechanism a K-map depends on — but that stops being geometrically possible once there are more than 4 variables to track on two axes. The standard fix is to split the extra variables into separate tiles instead of trying to force them onto the same grid, and adjacency between matching cells across tiles still counts exactly the same way it does within one tile. That last part is the piece most people miss the first time they see it.
How the split works
A 5-variable function splits into two 4-variable tiles, one for each value of the fifth variable — everything else about each tile (rows, columns, Gray code ordering) works exactly like a normal 4-variable map. A 6-variable function splits into four tiles, arranged in a 2×2 layout based on the two extra variables. Nothing about grouping within a single tile changes from the 4-variable case — the only new rule is what happens between tiles.
Cross-tile adjacency, worked
Take a 5-variable function where two cells sit in the exact same row/column position, one in each tile — say A′B′C′D′ with the fifth variable at 0 in one tile and 1 in the other. Those two cells are adjacent to each other, in exactly the same way two side-by-side cells in a single tile are adjacent, and they combine the same way: the fifth variable drops out, leaving A′B′C′D′ as a group covering both.
It also combines with in-tile adjacency at the same time. Take four minterms forming two adjacent pairs, one pair in each tile, sitting at matching positions: the group can drop two variables at once — both the in-tile variable that varies between the pair, and the tile variable that varies between the tiles. A real example: minterms 0, 1, 4, and 5 in a 5-variable function combine into a single group of four, reducing straight to A′B′D′ — one variable dropped from the in-tile pairing (C) and one from the cross-tile pairing (E), simultaneously.
6 variables: two tile-selector variables instead of one
With two extra variables, there are four tiles instead of two, and adjacency now runs in two separate directions: tiles that differ in only the first extra variable are adjacent, and tiles that differ in only the second extra variable are adjacent — but two tiles that differ in both extra variables at once are not adjacent to each other, the same way diagonal cells within a single K-map are never adjacent either. A group can still span all four tiles at once, though, if the same relative cell position is 1 in every tile — that's a valid group of four, dropping both extra variables in one step, exactly like a 4-cell group anywhere else on a map.
The practical takeaway
Everything you already know about grouping — power-of-2 sizes, preferring the largest valid rectangle, wraparound at the edges of each individual tile — still applies unchanged. The only genuinely new skill is checking the matching position across tiles before assuming a group stops at a tile's border. It's easy to under-simplify a 5- or 6-variable function purely by not looking across tiles, not because the math is actually harder.