n=12 R=120.0: 7485 reachable points, 118848 nodes, max #reflections 124, exact fallbacks 9748, mp calls 0, 7.2s
   types: A0:3428 A1:909 A2:463 A3:301 A4:241 A5:229 A6:241 A7:301 A8:463 A9:909
   alpha in [0,omega], beta in [2pi/n,pi] violated: 0
   Def 2.1 rows as printed (with parity rule) give exactly the exact-formula type: failures 0
   points where a row of the 'wrong' sign also holds: 11; of these with a DIFFERENT type from that row: 9
      these ambiguous points have N in [1] (N=1: the diagonals X_0X_{k+1}, 1<=k<=n-3: expected 9)
   X_0X_(k+1) has type A_k for 0<=k<=n-2: True
   remark 'A_0 <=> beta-alpha=2pi/n' fails for 0 non-diagonal points (for the 9 proper diagonals the remark is not literally true)
   remark 'middle type A_(m-1) <=> beta+alpha=pi' fails for 0 points
   (k mod 2, end label mod 2) histogram: {(0, 1): 4836, (1, 0): 2649}  [Prop. 2.2: k even <=> one class]
