> with(linalg): 
> with(ListTools):

> A1:= matrix(11,6,[[1,1,0,0,0,0],[1,0,1,0,0,0],
> [1,0,0,1,0,0],[1,0,0,0,1,0],
> [-1,1,0,0,0,0],[-1,0,1,0,0,0],
> [-1,0,0,1,0,0],[-1,0,0,0,1,0],
> [0,1,1,0,0,0],[0,1,0,1,0,0],[0,1,0,0,1,0]]); 
  
> A2:= matrix(13,6,[[0,-1,1,0,0,0],[0,-1,0,1,0,0],[0,-1,0,0,1,0],
> [0,0,1,1,0,0],[0,0,1,0,1,0],
> [0,0,-1,1,0,0],[0,0,-1,0,1,0],
> [0,0,0,1,1,0],[0,0,0,-1,1,0],
> [1/2,1/2,1/2,1/2,1/2,1/2],
> [-1/2,-1/2,1/2,1/2,1/2,1/2],
> [-1/2,1/2,-1/2,1/2,1/2,1/2],
> [-1/2,1/2,1/2,-1/2,1/2,1/2]]);

> A3:= matrix(13,6,[[-1/2,1/2,1/2,1/2,-1/2,1/2],
> [1/2,-1/2,-1/2,1/2,1/2,1/2],
> [1/2,-1/2,1/2,-1/2,1/2,1/2],
> [1/2,-1/2,1/2,1/2,-1/2,1/2],
> [1/2,1/2,-1/2,-1/2,1/2,1/2],
> [1/2,1/2,-1/2,1/2,-1/2,1/2], 
> [1/2,1/2,1/2,-1/2,-1/2,1/2],
> [-1/2,-1/2,-1/2,-1/2,1/2,1/2],
> [-1/2,-1/2,-1/2,1/2,-1/2,1/2],
> [-1/2,-1/2,1/2,-1/2,-1/2,1/2],
> [-1/2,1/2,-1/2,-1/2,-1/2,1/2],
> [1/2,-1/2,-1/2,-1/2,-1/2,1/2],
> [0,0,0,0,0,0]]);

> A:= stackmatrix(A1,A2,A3): rowdim(A); coldim(A); 
> Cnt:= 0; 
> ff:= proc(x)
> 	if irem(C[x,1],6)=0 then x;
> 	else 37;
> 	end if;
> end proc:

> for a from 0 by 2 to 5 do
> for b from 0 by 2 to 5 do
> for c from 0 by 2 to 5 do
> for d from 0 by 2 to 5 do
> for e from 0 by 2 to 5 do
> for f from 0 by 2 to 5 do
> e1:= (b-c)/2: e2:= (b+c)/2: 
> e3:= d+e2: e4:= e+e3: e5:= f+e4: 
> e6:= (2*a)-e1+e2+e3+e4+e5:
> B:= matrix(6,1,[[e1],[e2],[e3],[e4],[e5],[e6]]):
> C:= multiply(A,B):
> S:= seq(ff(i),i=1..37):
> L:= MakeUnique([S]):
> M:= submatrix(A,L,[1,2,3,4,5,6]):
> if rank(M)=6 then Cnt:=Cnt+1;
> end if:
> end do; end do; end do;
> end do; end do; end do;
> 
> Cnt;