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Just some random figures for now.
Facet count: 62592
nlgn: 691290
user 0m0.360s
Facet count: 7944
nlgn: 71338
user 0m0.030s
Facet count: 2892
nlgn: 23048
user 0m0.010s
These appear to be roughly in keeping with our back-of-the envelope
analysis that manifold checking can be done in NlogN.