JCSBimp's Hexagonal Orthogonal

Not all of the work is done yet, and the thought-work has just begun, but I wanted to update with a screenshot of the concept of the Initial Trapezoid: the quadrilateral bounded by the green and red lines where the Remainder Line in orange, passing through a typical pair of remainders r₀ and r₁, intersects the lines y=-x and y=x+1 which are boundaries in the Zone Grid I have constructed, all skewed left (linear transformation) from my initial conception without affecting the intersection points.

The calculations continue, and examination of possible derivations has not yet begun.