n=5: all 125 reachable points of radius <= 15.3117 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 16; number of reachable n-gons through them: {0: 6, 1: 10}  (never more than one)
      on NO reachable n-gon: w = (1, 2, 1, 1) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_1, |w| = 4.040574,  w = 3.618034 xi + 3.236068 eta, N = 3 segments
      on NO reachable n-gon: w = (1, 1, 2, 1) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_2, |w| = 4.040574,  w = 3.236068 xi + 3.618034 eta, N = 3 segments
      on NO reachable n-gon: w = (2, 3, 2, 1) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_1, |w| = 6.613822,  w = 6.236068 xi + 4.854102 eta, N = 5 segments
      on NO reachable n-gon: w = (1, 2, 3, 2) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_2, |w| = 6.613822,  w = 4.854102 xi + 6.236068 eta, N = 5 segments
  (c) u=xi, v=eta: the point xi + (lambda+1) eta is: reachable (type A_0);  xi + lambda^2 eta is: reachable (type A_0);  xi + (lambda^2-1) eta = X_2 is: reachable (type A_1)
n=6: all 175 reachable points of radius <= 18.0000 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 21; number of reachable n-gons through them: {0: 10, 1: 11}  (never more than one)
      on NO reachable n-gon: w = (1, 4) in the basis 1, z, ..., z^1 (z = exp(2 pi i/6)), type A_3, |w| = 4.582576,  w = 5.000000 xi + 4.000000 eta, N = 3 segments
      on NO reachable n-gon: w = (-1, 5) in the basis 1, z, ..., z^1 (z = exp(2 pi i/6)), type A_1, |w| = 4.582576,  w = 4.000000 xi + 5.000000 eta, N = 3 segments
      on NO reachable n-gon: w = (2, 4) in the basis 1, z, ..., z^1 (z = exp(2 pi i/6)), type A_2, |w| = 5.291503,  w = 6.000000 xi + 4.000000 eta, N = 3 segments
      on NO reachable n-gon: w = (-2, 6) in the basis 1, z, ..., z^1 (z = exp(2 pi i/6)), type A_2, |w| = 5.291503,  w = 4.000000 xi + 6.000000 eta, N = 3 segments
  (c) u=xi, v=eta: xi + (lambda+1) eta is not in Z[zeta_n] (lambda = 2cos(pi/n) is not in Q(zeta_n) for even n), hence not a vertex of the development;  xi + lambda^2 eta is: reachable (type A_0)
n=7: all 235 reachable points of radius <= 20.7429 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 26; number of reachable n-gons through them: {0: 14, 1: 12}  (never more than one)
      on NO reachable n-gon: w = (2, 0, 3, 0, 1, 0) in the basis 1, z, ..., z^5 (z = exp(2 pi i/14)), type A_4, |w| = 4.932822,  w = 6.295897 xi + 4.246980 eta, N = 3 segments
      on NO reachable n-gon: w = (0, 1, 0, 3, 0, 2) in the basis 1, z, ..., z^5 (z = exp(2 pi i/14)), type A_1, |w| = 4.932822,  w = 4.246980 xi + 6.295897 eta, N = 3 segments
      on NO reachable n-gon: w = (1, 2, 1, 2, 1, 1) in the basis 1, z, ..., z^5 (z = exp(2 pi i/14)), type A_2, |w| = 6.151128,  w = 7.295897 xi + 6.850855 eta, N = 3 segments
      on NO reachable n-gon: w = (3, 0, 3, 0, 2, -1) in the basis 1, z, ..., z^5 (z = exp(2 pi i/14)), type A_3, |w| = 6.151128,  w = 7.850855 xi + 4.493959 eta, N = 3 segments
  (c) u=xi, v=eta: the point xi + (lambda+1) eta is: not_a_vertex;  xi + lambda^2 eta is: reachable (type A_0);  xi + (lambda^2-1) eta = X_2 is: reachable (type A_1)
n=8: all 299 reachable points of radius <= 23.5181 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 23; number of reachable n-gons through them: {0: 12, 1: 11}  (never more than one)
      on NO reachable n-gon: w = (2, 3, 1, 0) in the basis 1, z, ..., z^3 (z = exp(2 pi i/8)), type A_5, |w| = 5.169905,  w = 7.242641 xi + 4.414214 eta, N = 3 segments
      on NO reachable n-gon: w = (0, 1, 3, 2) in the basis 1, z, ..., z^3 (z = exp(2 pi i/8)), type A_1, |w| = 5.169905,  w = 4.414214 xi + 7.242641 eta, N = 3 segments
      on NO reachable n-gon: w = (2, 3, 3, 1) in the basis 1, z, ..., z^3 (z = exp(2 pi i/8)), type A_4, |w| = 6.754807,  w = 9.242641 xi + 8.242641 eta, N = 3 segments
      on NO reachable n-gon: w = (-1, 2, 3, 3) in the basis 1, z, ..., z^3 (z = exp(2 pi i/8)), type A_2, |w| = 6.754807,  w = 4.828427 xi + 9.242641 eta, N = 3 segments
  (c) u=xi, v=eta: xi + (lambda+1) eta is not in Z[zeta_n] (lambda = 2cos(pi/n) is not in Q(zeta_n) for even n), hence not a vertex of the development;  xi + lambda^2 eta is: reachable (type A_0)
n=9: all 363 reachable points of radius <= 26.3142 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 26; number of reachable n-gons through them: {0: 14, 1: 12}  (never more than one)
      on NO reachable n-gon: w = (2, 0, 3, 0, 1, 0) in the basis 1, z, ..., z^5 (z = exp(2 pi i/18)), type A_6, |w| = 5.336983,  w = 7.943563 xi + 4.532089 eta, N = 3 segments
      on NO reachable n-gon: w = (0, -2, 0, 1, 2, 3) in the basis 1, z, ..., z^5 (z = exp(2 pi i/18)), type A_1, |w| = 5.336983,  w = 4.532089 xi + 7.943563 eta, N = 3 segments
      on NO reachable n-gon: w = (3, 1, 3, 0, 1, 0) in the basis 1, z, ..., z^5 (z = exp(2 pi i/18)), type A_5, |w| = 7.190498,  w = 10.290859 xi + 5.064178 eta, N = 3 segments
      on NO reachable n-gon: w = (1, 0, 3, 1, 3, 0) in the basis 1, z, ..., z^5 (z = exp(2 pi i/18)), type A_5, |w| = 7.190498,  w = 11.170245 xi + 8.943563 eta, N = 3 segments
  (c) u=xi, v=eta: the point xi + (lambda+1) eta is: not_a_vertex;  xi + lambda^2 eta is: reachable (type A_0);  xi + (lambda^2-1) eta = X_2 is: reachable (type A_1)
n=10: all 443 reachable points of radius <= 29.1246 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 23; number of reachable n-gons through them: {0: 12, 1: 11}  (never more than one)
      on NO reachable n-gon: w = (2, 3, 1, 0) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_7, |w| = 5.458789,  w = 8.472136 xi + 4.618034 eta, N = 3 segments
      on NO reachable n-gon: w = (-2, 2, -1, 5) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_1, |w| = 5.458789,  w = 4.618034 xi + 8.472136 eta, N = 3 segments
      on NO reachable n-gon: w = (4, 2, 3, -1) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_6, |w| = 7.513378,  w = 11.090170 xi + 5.236068 eta, N = 3 segments
      on NO reachable n-gon: w = (2, 3, 3, 1) in the basis 1, z, ..., z^3 (z = exp(2 pi i/10)), type A_6, |w| = 7.513378,  w = 12.708204 xi + 9.472136 eta, N = 3 segments
  (c) u=xi, v=eta: xi + (lambda+1) eta is not in Z[zeta_n] (lambda = 2cos(pi/n) is not in Q(zeta_n) for even n), hence not a vertex of the development;  xi + lambda^2 eta is: reachable (type A_0)
n=11: all 533 reachable points of radius <= 31.9452 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 20; number of reachable n-gons through them: {0: 8, 1: 12}  (never more than one)
      on NO reachable n-gon: w = (2, 0, 3, 0, 1, 0, 0, 0, 0, 0) in the basis 1, z, ..., z^9 (z = exp(2 pi i/22)), type A_8, |w| = 5.550155,  w = 8.878351 xi + 4.682507 eta, N = 3 segments
      on NO reachable n-gon: w = (0, 0, 0, 0, 0, 1, 0, 3, 0, 2) in the basis 1, z, ..., z^9 (z = exp(2 pi i/22)), type A_1, |w| = 5.550155,  w = 4.682507 xi + 8.878351 eta, N = 3 segments
      on NO reachable n-gon: w = (2, 0, 3, 0, 3, 0, 1, 0, 0, 0) in the basis 1, z, ..., z^9 (z = exp(2 pi i/22)), type A_7, |w| = 7.758437,  w = 13.937889 xi + 9.878351 eta, N = 3 segments
      on NO reachable n-gon: w = (-1, 0, 0, 0, 0, 2, 0, 3, 0, 3) in the basis 1, z, ..., z^9 (z = exp(2 pi i/22)), type A_2, |w| = 7.758437,  w = 5.365014 xi + 11.709181 eta, N = 3 segments
  (c) u=xi, v=eta: the point xi + (lambda+1) eta is: not_a_vertex;  xi + lambda^2 eta is: reachable (type A_0);  xi + (lambda^2-1) eta = X_2 is: reachable (type A_1)
n=12: all 641 reachable points of radius <= 34.7733 enumerated (needed for points w with |w| <= 9.0)
  (a) reachable n-gons through X_2 (type A_1): 1; the only one is P_0 itself: True
  (b) reachable points of type != A_0 and radius <= 9.0: 21; number of reachable n-gons through them: {0: 8, 1: 13}  (never more than one)
      on NO reachable n-gon: w = (2, 3, 1, 0) in the basis 1, z, ..., z^3 (z = exp(2 pi i/12)), type A_9, |w| = 5.620361,  w = 9.196152 xi + 4.732051 eta, N = 3 segments
      on NO reachable n-gon: w = (-3, -2, 3, 3) in the basis 1, z, ..., z^3 (z = exp(2 pi i/12)), type A_1, |w| = 5.620361,  w = 4.732051 xi + 9.196152 eta, N = 3 segments
      on NO reachable n-gon: w = (-3, -2, 4, 5) in the basis 1, z, ..., z^3 (z = exp(2 pi i/12)), type A_2, |w| = 7.948391,  w = 10.196152 xi + 14.928203 eta, N = 3 segments
      on NO reachable n-gon: w = (-4, -3, 3, 5) in the basis 1, z, ..., z^3 (z = exp(2 pi i/12)), type A_2, |w| = 7.948391,  w = 5.464102 xi + 12.196152 eta, N = 3 segments
  (c) u=xi, v=eta: xi + (lambda+1) eta is not in Z[zeta_n] (lambda = 2cos(pi/n) is not in Q(zeta_n) for even n), hence not a vertex of the development;  xi + lambda^2 eta is: reachable (type A_0)
