n=27: 279 reachable points with |B|<=24, 64 direction classes
distinct patterns: class | (preclosed length / shortest , reduced factor) ... | unreduced factor tuples -> number of direction classes
  class -    | 1.00000:x1  1.98648:x1  2.94609:x1  3.86586:x1  4.73336:x1  5.53684:x1  6.26544:x1  6.90932:x1  7.45976:x1  7.90932:x1  8.25192:x1  8.48293:x1  8.59922:x1 | {(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1): 1} | n among reduced factors: False
  class -    | 1.00000:x3  1.98648:x3  2.94609:x1  3.86586:x3  4.73336:x3  5.53684:x1  6.26544:x3  6.90932:x3  7.45976:x1  7.90932:x3  8.25192:x3  8.48293:x1  8.59922:x3 | {(3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3): 3} | n among reduced factors: False
  class -    | 1.00000:x9  1.98648:x9  2.94609:x3  3.86586:x9  4.73336:x9  5.53684:x3  6.26544:x9  6.90932:x9  7.45976:x1  7.90932:x9  8.25192:x9  8.48293:x3  8.59922:x9 | {(27, 27, 9, 27, 27, 9, 27, 27, 3, 27, 27, 9, 27): 49, (9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9): 11} | n among reduced factors: False
longest closed trajectory met: 1350 bounces
direction classes with a reduced factor equal to n: 0 of 64
Theorem 7(b) on these direction classes: classes 64 ; with exactly m=13 bands of distinct preclosed length: 64 ; preclosed lengths proportional to sin(2j pi/n): 64 ; factors = n/gcd(n, alpha*j) for some alpha: 64 ; gcd(alpha, n) -> number of classes: {1: 49, 3: 11, 9: 3, 27: 1}
exact decisions: 329658, time 23.0s
