Switch off every light. Clicking a tile toggles it and every tile it touches — on any tiling you like.
Tiling
Board size
Neighbours
Edges
Game
Shape
Right-click a tile to remove it, or turn on Edit shape and drag across as many as you like — starting on a tile removes, starting on a hole puts back. Removing clears the lights; New puzzle deals a position on the shape you have made. Changing tiling, size or edges starts it over.
The rules never change — only the shape of the neighbourhood. Adjacency is derived from which tiles share an edge, so every tiling below runs on the same engine and the same solver.