n=8 R=30.0: 469 reachable points, 2970 nodes, max #reflections 32, exact fallbacks 860, mp calls 0, 0.1s
   types: A0:226 A1:67 A2:37 A3:35 A4:37 A5:67
   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: 7; of these with a DIFFERENT type from that row: 5
      these ambiguous points have N in [1] (N=1: the diagonals X_0X_{k+1}, 1<=k<=n-3: expected 5)
   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 5 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): 300, (1, 0): 169}  [Prop. 2.2: k even <=> one class]
