PROCEDURE SetOnext(a, b: Arc);
(* If Onext(a) # b, performs Splice(a, Oprev(b)).  
   After this call, Onext(a) will be equal to b.
   Valid whenever Splice(a,b) is valid. *)

(*
  Conjecture: let e[0..n] be all Arc's of an Oct structure
  with FlipBit = 0; and x[0..n] a list of arcs 
  such that Onext(e[i]) = x[i].
  
  We can build a copy of the structure by the following
  algorithm:
  
    1. create n/4 new Edge's, and a vector ec[0..n] of
       their unFlipped Arc's, such that
         (a) if Rot(e[i]) = e[j], then Rot(ec[i]) = ec[j]
         
    2. Create a vector xc[0..n] of Arc's, such that if 
       x[i] = Flip^f(e[j]), then xc[i] = Flip^f(ec[j]).
    
    3. for i = 0..n, in any order, perform SetOnext(ec[i], xc[i]).
    
  This conjecture is true if we can prove that 
  
    every Arc has its Onext properly set;
    
    whenever SetOnext(ec[i], ec[x[i]]) changes Onext(e[j])
    for some arc j, then we still haven't performed 
    SetOnext(ec[j], ec[x[j]]).
    
*)