face list: consistent orientation, 20 vertices, 30 edges; distances from vertex 0: {0: 0, 1: 2, 2: 2, 3: 3, 4: 2, 5: 3, 6: 3, 7: 5, 8: 1, 9: 3, 10: 2, 11: 4, 12: 1, 13: 3, 14: 2, 15: 4, 16: 1, 17: 2, 18: 3, 19: 4}
reachable points of the pentagon with |B| <= 19 in the full sector: 187
points with |B|^2 = (307+137 sqrt5)/2 = 306.670656459: 4
  B = 15.017221+9.008537i, slope angle alpha = 0.540332 rad = 0.1720 pi, N = 16, end vertex 2 (distance 2), last face 1
    face word: [1, 3, 9, 11, 10, 8, 6, 4, 2, 1, 9, 10, 8, 4, 2, 1]
    crossed edges: [(2, 16), (2, 13), (13, 15), (7, 15), (7, 19), (5, 19), (5, 14), (1, 12), (0, 16), (2, 10), (6, 15), (7, 19), (5, 9), (1, 12), (0, 16)]
    identical to the published witness (face word and crossed edges): False
    exact check 2|B|^2 = 307 + 137 sqrt5: True
    N is even. End vertex 2; its neighbours in the last face: plane-ccw-next 10, plane-cw-next 16
    reading of the source (N even -> mirror image of the oriented table, outgoing edge = plane-clockwise one):
        beta = 0.9720 pi, beta - alpha = 0.8000 pi  = 2.0000 * (2pi/5)
        type by Def. 2.1 (my implementation type_of): A_1
    reading that ignores the reversal of orientation (outgoing edge = plane-counterclockwise one, as for N odd):
        beta' = 0.4280 pi, beta' - alpha = 0.2560 pi = 0.6400 * (2pi/5), beta' + alpha = 0.6000 pi = 1.5000 * (2pi/5)
        -S0/S1 for S1 = plane-ccw outgoing edge: arg = 0.4000 pi (eta^2 has arg 0.4 pi)
        -S0/S1 for S1 = plane-cw outgoing edge: arg = -0.2000 pi (eta^2 has arg 0.4 pi)
  B = 17.444272+1.538842i, slope angle alpha = 0.087987 rad = 0.0280 pi, N = 16, end vertex 2 (distance 2), last face 1
    face word: [1, 3, 11, 8, 6, 5, 1, 3, 11, 10, 8, 6, 4, 5, 2, 1]
    crossed edges: [(2, 16), (3, 13), (7, 11), (5, 19), (4, 14), (0, 8), (2, 16), (3, 13), (7, 15), (7, 19), (5, 19), (5, 14), (12, 14), (0, 12), (0, 16)]
    identical to the published witness (face word and crossed edges): True
    exact check 2|B|^2 = 307 + 137 sqrt5: True
    N is even. End vertex 2; its neighbours in the last face: plane-ccw-next 10, plane-cw-next 16
    reading of the source (N even -> mirror image of the oriented table, outgoing edge = plane-clockwise one):
        beta = 0.8280 pi, beta - alpha = 0.8000 pi  = 2.0000 * (2pi/5)
        type by Def. 2.1 (my implementation type_of): A_1
    reading that ignores the reversal of orientation (outgoing edge = plane-counterclockwise one, as for N odd):
        beta' = 0.5720 pi, beta' - alpha = 0.5440 pi = 1.3600 * (2pi/5), beta' + alpha = 0.6000 pi = 1.5000 * (2pi/5)
        -S0/S1 for S1 = plane-ccw outgoing edge: arg = 0.4000 pi (eta^2 has arg 0.4 pi)
        -S0/S1 for S1 = plane-cw outgoing edge: arg = -0.2000 pi (eta^2 has arg 0.4 pi)
  B = -3.927051+17.066017i, slope angle alpha = 1.796969 rad = 0.5720 pi, N = 16, end vertex 10 (distance 2), last face 1
    face word: [1, 0, 10, 8, 7, 2, 1, 0, 10, 11, 8, 7, 4, 2, 5, 1]
    crossed edges: [(8, 10), (6, 18), (7, 19), (9, 11), (1, 17), (0, 16), (8, 10), (6, 18), (7, 15), (7, 11), (9, 11), (1, 9), (1, 12), (0, 12), (0, 8)]
    identical to the published witness (face word and crossed edges): False
    exact check 2|B|^2 = 307 + 137 sqrt5: True
    N is even. End vertex 10; its neighbours in the last face: plane-ccw-next 8, plane-cw-next 2
    reading of the source (N even -> mirror image of the oriented table, outgoing edge = plane-clockwise one):
        beta = 0.5720 pi, beta - alpha = -0.0000 pi  = -0.0000 * (2pi/5)
        type by Def. 2.1 (my implementation type_of): A_2
    reading that ignores the reversal of orientation (outgoing edge = plane-counterclockwise one, as for N odd):
        beta' = 0.8280 pi, beta' - alpha = 0.2560 pi = 0.6400 * (2pi/5), beta' + alpha = 1.4000 pi = 3.5000 * (2pi/5)
        -S0/S1 for S1 = plane-ccw outgoing edge: arg = -0.4000 pi (eta^2 has arg 0.4 pi)
        -S0/S1 for S1 = plane-cw outgoing edge: arg = 1.0000 pi (eta^2 has arg 0.4 pi)
  B = 3.927051+17.066017i, slope angle alpha = 1.344624 rad = 0.4280 pi, N = 16, end vertex 10 (distance 2), last face 1
    face word: [1, 0, 9, 10, 11, 8, 7, 4, 5, 1, 9, 11, 8, 4, 5, 1]
    crossed edges: [(8, 10), (6, 10), (6, 15), (7, 15), (7, 11), (9, 11), (1, 9), (12, 14), (0, 8), (2, 10), (13, 15), (7, 11), (5, 9), (12, 14), (0, 8)]
    identical to the published witness (face word and crossed edges): False
    exact check 2|B|^2 = 307 + 137 sqrt5: True
    N is even. End vertex 10; its neighbours in the last face: plane-ccw-next 8, plane-cw-next 2
    reading of the source (N even -> mirror image of the oriented table, outgoing edge = plane-clockwise one):
        beta = 0.4280 pi, beta - alpha = -0.0000 pi  = -0.0000 * (2pi/5)
        type by Def. 2.1 (my implementation type_of): A_2
    reading that ignores the reversal of orientation (outgoing edge = plane-counterclockwise one, as for N odd):
        beta' = 0.9720 pi, beta' - alpha = 0.5440 pi = 1.3600 * (2pi/5), beta' + alpha = 1.4000 pi = 3.5000 * (2pi/5)
        -S0/S1 for S1 = plane-ccw outgoing edge: arg = -0.4000 pi (eta^2 has arg 0.4 pi)
        -S0/S1 for S1 = plane-cw outgoing edge: arg = 1.0000 pi (eta^2 has arg 0.4 pi)
all short geodesics from vertex 0 (first face F1, full sector) to vertex 2 with length <= 19: (length, N, type)
   [(1.618, 1, 2), (9.2123, 7, 2), (9.2123, 7, 2), (17.0438, 13, 2), (17.0438, 13, 2), (17.512, 16, 1), (17.512, 16, 1), (18.0448, 16, 1), (18.0448, 16, 1)]
types of ALL geodesics of length <= 19 ending at distance 2: [1, 2] ; ending distances of all type-A_0 ones: [1, 3, 4, 5]
