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Achernar's pieces can conditionally switch to squares in a different rank at option, in lieu of a move. Would not that kernel of an idea be better embodied in a 3-D version? Relying on adjacency, variously defined, 3-D Chesses more or less try to extend 2-D notions(motions) to 3-D. Instead, think of a piece's moving to, say, the perimeter of a 2-D board, then being able to 'advance' to overlaying or underlying game board(s) (3-D levels) to a number of squares a la Achernar. Achernar certainly has unrealized potential if the too-numerous piece enhancements were scaled back. Hypothetical three-dimensional Chesses, relying on positional as opposed to motional criteria, would retroactively broadly include the fifty-year-old Alice Chess (though not 100-year-old Kriegspiel)too as notionally 3-D.