# T12: for every piece of every section X(G) ∩ {x_i = alpha}, an elementary collapse
# sequence to a vertex (2D cell notation u,v:D in the two remaining coordinates, in
# increasing order of axes; for half-integer alpha, u,v:- is the crossing edge with
# lower end at that position, u,v:u a crossing square, u,v:uv a crossing cube)
PIECE axis=x alpha=0.0 V=4 E=4 F=1 collapsible=True -> 1,1:-
  0,0:u ; 0,0:uv
  0,0:- ; 0,0:v
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
PIECE axis=x alpha=0.5 V=4 E=3 F=0 collapsible=True -> 1,1:-
  0,0:- ; 0,0:u
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
PIECE axis=x alpha=1.0 V=4 E=3 F=0 collapsible=True -> 1,1:-
  0,0:- ; 0,0:u
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
PIECE axis=x alpha=1.5 V=4 E=3 F=0 collapsible=True -> 1,1:-
  0,0:- ; 0,0:u
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
PIECE axis=x alpha=2.0 V=4 E=4 F=1 collapsible=True -> 1,1:-
  0,0:u ; 0,0:uv
  0,0:- ; 0,0:v
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
PIECE axis=y alpha=0.0 V=6 E=6 F=0 collapsible=False -> 0,0:- 0,0:u 0,0:v 0,1:- 0,1:u 1,0:- 1,0:u 1,1:- 1,1:u 2,0:- 2,0:v 2,1:-
PIECE axis=y alpha=0.5 V=6 E=6 F=0 collapsible=False -> 0,0:- 0,0:u 0,0:v 0,1:- 0,1:u 1,0:- 1,0:u 1,1:- 1,1:u 2,0:- 2,0:v 2,1:-
PIECE axis=y alpha=1.0 V=6 E=7 F=2 collapsible=True -> 2,1:-
  0,0:u ; 0,0:uv
  1,0:u ; 1,0:uv
  0,0:- ; 0,0:v
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
  1,1:- ; 1,1:u
  2,0:- ; 2,0:v
PIECE axis=z alpha=0.0 V=6 E=7 F=2 collapsible=True -> 2,1:-
  0,0:u ; 0,0:uv
  1,0:u ; 1,0:uv
  0,0:- ; 0,0:v
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
  1,1:- ; 1,1:u
  2,0:- ; 2,0:v
PIECE axis=z alpha=0.5 V=5 E=4 F=0 collapsible=True -> 2,1:-
  0,0:- ; 0,0:v
  0,1:- ; 0,1:u
  1,1:- ; 1,1:u
  2,0:- ; 2,0:v
PIECE axis=z alpha=1.0 V=6 E=7 F=2 collapsible=True -> 2,1:-
  0,0:u ; 0,0:uv
  1,0:u ; 1,0:uv
  0,0:- ; 0,0:v
  0,1:- ; 0,1:u
  1,0:- ; 1,0:v
  1,1:- ; 1,1:u
  2,0:- ; 2,0:v
