n=21: 439 reachable points with |B|<=30, 102 direction classes
distinct patterns: class | (preclosed length / shortest , reduced factor) ... | unreduced factor tuples -> number of direction classes
  class -    | 1.00000:x1  1.97766:x1  2.91115:x1  3.77960:x1  4.56362:x1  5.24570:x1  5.81060:x1  6.24570:x1  6.54128:x1  6.69074:x1 | {(1, 1, 1, 1, 1, 1, 1, 1, 1, 1): 3} | n among reduced factors: False
  class -    | 1.00000:x1  1.97766:x1  2.91115:x1  3.77960:x1  4.56362:x1  5.24570:x1  5.81060:x1  6.24570:x1  6.54128:x1  6.69075:x1 | {(1, 1, 1, 1, 1, 1, 1, 1, 1, 1): 3} | n among reduced factors: False
  class -    | 1.00000:x3  1.97766:x3  2.91115:x1  3.77960:x3  4.56362:x3  5.24570:x1  5.81060:x3  6.24570:x3  6.54128:x1  6.69074:x3 | {(3, 3, 1, 3, 3, 1, 3, 3, 1, 3): 1} | n among reduced factors: False
  class -    | 1.00000:x3  1.97766:x3  2.91115:x1  3.77960:x3  4.56362:x3  5.24570:x1  5.81060:x3  6.24570:x3  6.54128:x1  6.69075:x3 | {(3, 3, 1, 3, 3, 1, 3, 3, 1, 3): 3} | n among reduced factors: False
  class -    | 1.00000:x7  1.97766:x7  2.91115:x7  3.77960:x7  4.56362:x7  5.24570:x7  5.81060:x1  6.24570:x7  6.54128:x7  6.69074:x7 | {(7, 7, 7, 7, 7, 7, 1, 7, 7, 7): 12} | n among reduced factors: False
  class -    | 1.00000:x7  1.97766:x7  2.91115:x7  3.77960:x7  4.56362:x7  5.24570:x7  5.81060:x1  6.24570:x7  6.54128:x7  6.69075:x7 | {(7, 7, 7, 7, 7, 7, 1, 7, 7, 7): 6} | n among reduced factors: False
  class -    | 1.00000:x21  1.97766:x21  2.91115:x7  3.77960:x21  4.56362:x21  5.24570:x7  5.81060:x3  6.24570:x21  6.54128:x7  6.69074:x21 | {(21, 21, 7, 21, 21, 7, 3, 21, 7, 21): 36} | n among reduced factors: True
  class -    | 1.00000:x21  1.97766:x21  2.91115:x7  3.77960:x21  4.56362:x21  5.24570:x7  5.81060:x3  6.24570:x21  6.54128:x7  6.69075:x21 | {(21, 21, 7, 21, 21, 7, 3, 21, 7, 21): 38} | n among reduced factors: True
longest closed trajectory met: 1638 bounces
direction classes with a reduced factor equal to n: 74 of 102
Theorem 7(b) on these direction classes: classes 102 ; with exactly m=10 bands of distinct preclosed length: 102 ; preclosed lengths proportional to sin(2j pi/n): 102 ; factors = n/gcd(n, alpha*j) for some alpha: 102 ; gcd(alpha, n) -> number of classes: {1: 74, 3: 18, 7: 4, 21: 6}
exact decisions: 278642, time 19.4s
