Hi Adrian and All,
Back in 2017 I first tried making fullerenes with fullgen, got a bit
carried away and made them all the way up to 140 vertices. I remember it
took weeks.
Subsequently we worked on canonical and other features. Getting the
material back together, I rebuilt them.
The motive for doing it was that I tested the old models and most of
them didn't pass being canonical even at 1e-11. I wondered how the new
algorithm would work and it turns out it works very nicely.
I canonicalized them at -l 17 using a limit of -n 5000. An exact n is
arbitrary because at -l 17 the model will jitter and never come to an
actual completion so n stops it. Much of the time it would do a whole
set of vertices passing at -l 17, and if not, a dozen or two could be
finished at -n 10000. Running these loops took very little time.
This is impressive (we are talking 425,376 models here!) and some of
them are tubular but it did them anyway at -n 5000. All of them, if
trying to rerun straight canonical (-l 12) on them, will find them
already canonicalized.
Working at such a fine limit I expect some problems and there were. All
of these find a symmetry of C2. I wasn't going to mention it because
they all have long and also very short edges, however I noticed all them
had to do with D symmetry. Perhaps if you wanted to look into it
sometime it might narrow it down.
fg120/D5v/fg120_00000001.off
fg132/D2/fg132_00014115.off
fg134/D3h/fg134_00008879.off
fg136/D2/fg136_00017241.off
fg140/D5v/fg140_00000001.off
fg140/D3v/fg140_00018411.off
fg140/D2/fg140_00018850.off
fg138/C2/fg138_00010566.off stubbornly would not pass at -l 17, even up
to -n 50000 and at least 1 edge pair wouldn't cross withing precision. I
ran -n 5000 to 50000 over night to see if I could hit a number where it
would work but it never passed (it does at -l 16). That model is
interesting because it is a spiral end to end.
It is also where I found that if it is rotated an arbitrary way, convex
hull can break a face or two. (I attached the models being mentioned)
off_util fg138_00010566.off | conv_hull | off_report
off_util fg138_00010566.off | off_trans -R 10,20,30 | conv_hull | off_report
I generated the model(s), zeroing out the vertices with -S 0 first for
consistency.
off_trans -S 0 fg138_00010566.off | poly_form -a u -l 0 -n 100000 -s 10
-z -1 | canonical -l 17 -n 5000 -z -1 -Y > tmp.off
The full sets are are here on my polyhedra dedicated google drive.
fullerenes_c20_c80.7z
https://drive.google.com/file/d/11u8nMoBSjEGKKnCgCNo547USQyBVsmkx/view?usp=share_link
fullerenes_c82_c140.7z
https://drive.google.com/file/d/1guEa0SPEDWDZuUWGIiGewCTIKwc2QoaG/view?usp=share_link
Roger