Case 1: If x_S ≠ x_D, y_S ≠ y_D, and z_S ≠ z_D

3 Routing vectors of L_opt length

R_1,1 = (−x)*(−y)*(−z)*,

R_1,2 = (−y)*(−z)*(−x)*,

R_1,3 = (−z)*(−x)*(−y)*

One routing vector of (L_opt + 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_opt length

R_2,1 = (−x)*(−y)*, R_2,2 = (−y)*(−x)*

One routing vector of (L_opt + 2) length

R_2,4 = z−(−x)*(−y)*z+

One routing vector of (L_opt + 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−