Magic Hypercube - Pathfinders

J. R. Hendricks called the directions within a hypercubes "pathfinders", these directions are simplest denoted in a ternary number system as:

Pfp where: p = k=0∑n-1 (ki + 1) 3k <==> <ki> ; i ε {-1,0,1}

This gives 3n directions. since every direction is traversed both ways one can limit to the upper half of the full range.

With these pathfinders any line to be summed over (or r-agonal) can be specified:

< j1 kθ l0 ; θ ε {-1,1} > ; p,q ε

which specifies all (broken) r-agonals, p and q ranges could be omitted from this description. The main (unbroken) r-agonals are thus given by the slight modification of the above:

< j1 k1 l-1 s0 >

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