Case 1: If x_{S} ≠ x_{D}, y_{S} ≠ y_{D}, and z_{S} ≠ z_{D} 3 Routing vectors of L_{op}_{t} length R_{1,1} = (−x)*(−y)*(−z)*, R_{1,2} = (−y)*(−z)*(−x)*, R_{1,3} = (−z)*(−x)*(−y)* One routing vector of (L_{op}_{t} + 4) length R_{1,4} = +x (−y)* (−z)* (−x)* | Case 2: If x_{S} ≠ x_{D}, y_{S} ≠ y_{D}, and z_{S} = z_{D} 2 routing vectors of L_{op}_{t} length R_{2,1} = (−x)*(−y)*, R_{2,2} = (−y)*(−x)* One routing vector of (L_{op}_{t} + 2) length R_{2,4} = z−(−x)*(−y)*z+ One routing vector of (L_{op}_{t} + 4) length R_{2,5} = +x (−y)*+ (−x)*−y |

Case 3: If x_{S} ≠ x_{D}, y_{S} = y_{D}, and z_{S} ≠ z_{D} 2 routing vectors of L_{opt} length R_{3,1} = (−x)*(−z)*, R_{3,2} = (−z)*(−x)* 2 routing vectors of (L_{opt} + 2) length R_{3,3} = y+ (−x)*(−z)*y−, R_{3,4} = y− (−x)*(−z)*y+ | Case 4: If x_{S} ≠ x_{D}, y_{S} = y_{D}, and z_{S} = z_{D} One routing vector of L_{opt} length R_{4,1} = (−x)* 3 routing vectors of (L_{opt} + 2) length R_{4,2} = y+ (−x)*y−, R_{4,3} = y− (−x)*y+, R_{4,5} = z− (−x)*z+ |

Case 5: If x_{S} = x_{D}, y_{S} ≠ y_{D}, and z_{S} ≠ z_{D} 2 routing vectors L_{opt} length R_{5,1} = (−y)* (−z)*, R_{5,2} = (−z)* (−y)* 2 routing vectors of (L_{opt} + 2) length R_{5,3} = x+ (−y)*(−z)*x−, R_{5,4} = x− (−y)*(−z)*x+ | Case 6: If x_{S} = x_{D}, y_{S} ≠ y_{D}, and z_{S} = z_{D} One routing vector of L_{opt} length R_{6,1} = (−y)* 3 routing vectors of (L_{opt} + 2) length R_{6,2} = x+ (−y)*x−, R_{6,3} = x− (−y)*x+, R_{6,5} = z− (−y)*z+ |

Case 7: If x_{S} = x_{D}, y_{S} = y_{D}, and z_{S} ≠ z_{D} One routing vector of L_{opt} length R_{7,1} = (−z)* 3 Routing vectors of (L_{opt} + 2) length R_{7,2} = x+ (−z)*x−, R_{7,3 }= x− (−z)*x+, R_{7,4} = y+ (−z)*y− | |