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Check out McCooey's Hexagonal Chess, our featured variant for May, 2025.
The diagram with all the diagonal lines is too busy to be helpful, I think.
The notation would probably be better off without repeating the names of rows; I don't think the benefit of giving the consistent name to the orthogonal line is worth making the cell names non-unique.
The third bishop move diagram seems to be missing a marker at g9. If a bishop is on a6, does it move through b5(6?), c4(6?), d3(6?), then chooses between e7-f8-g9 or e2-f1-g0?
Your castling diagrams use black pieces the same color as the board, making it hard to see.
I don't think saying "knight moves one hippogonally" is enough. "Hippogonal" literally means knightwise, but that needs description for a new board.
Pawns can capture backwards? Please add that to the diagram then. What about diagonally "sideways", as in the triangular cells? En passant is allowed for triple and quadruple initial steps, in "the obvious" way?