Exact rational vertices (x, y, z):
  v0 = (32000/251073, 7000/251073, 248927/251073)
  v1 = (610000/1226981, 732000/1226981, 773019/1226981)
  v2 = (86500/206577, 182500/206577, 43423/206577)
  v3 = (63000/511369, 137000/511369, 488631/511369)
  v4 = (-158000/1011141, -140000/1011141, 988859/1011141)
  v5 = (86200/125181, -51400/125181, 74819/125181)
  v6 = (802000/1167857, -168000/1167857, 832143/1167857)
EXACT CHECKS PASSED: on S^2, z > 0, all longitude gaps in (0, pi), winding number 1 => polar graph.
Edge lengths l_i (balls):
  l0 = [0.7888960631491880120775656 +/- 4.36e-26]
  l1 = [0.5203246524735021582669539 +/- 1.44e-27]
  l2 = [1.059709072629907850406866 +/- 1.80e-26]
  l3 = [0.4988494499224446746552389 +/- 2.77e-26]
  l4 = [1.007747884058091704549521 +/- 3.40e-25]
  l5 = [0.2914633818585299378202212 +/- 4.90e-26]
  l6 = [0.6600477045583841969592444 +/- 4.86e-26]
Signed turning angles tau_i (balls):
  tau0 = [-1.917573753423170417090627 +/- 1.86e-25]
  tau1 = [0.3996688062736972568768650 +/- 1.15e-26]
  tau2 = [2.737397626101988088933344 +/- 2.70e-25]
  tau3 = [-0.1637580559964382256565840 +/- 4.14e-26]
  tau4 = [1.762853468189857035471983 +/- 2.01e-25]
  tau5 = [1.986779351881962574772236 +/- 3.37e-25]
  tau6 = [1.049457433073317079422265 +/- 6.15e-26]
sum tau_i = [5.854824876101213392729483 +/- 3.94e-26]; fan area = [0.4283604310783730841958038 +/- 5.87e-27]; sum + area = [6.28318530717958647692528676656 +/- 9.95e-31]
Gauss-Bonnet check (sum + area contains 2 pi): True
cut at vertex 0: crossing pairs = [(0, 6)], undecided = []
  segments 0 and 6: orientation signs [-1, 1, 1, -1] (certain); endpoint distances to the other line: ['[0.592567215407 +/- 2.49e-13]', '[0.0652851388669 +/- 1.87e-14]', '[0.0526754154249 +/- 3.66e-14]', '[0.733596741626 +/- 4.59e-13]']
cut at vertex 1: crossing pairs = [], undecided = []
cut at vertex 2: crossing pairs = [], undecided = []
cut at vertex 3: crossing pairs = [], undecided = []
cut at vertex 4: crossing pairs = [], undecided = []
cut at vertex 5: crossing pairs = [], undecided = []
cut at vertex 6: crossing pairs = [], undecided = []
Adjacent-edge check: all |tau_i| < pi (no fold-back) certified.
CERTIFICATE COMPLETE: True
