show/hide visualization coordinates
a : (0.46456307988964435, -0.3986658860002822, 0.048234611431102914)
b : (-0.09646553471837749, -1.1025015291304376, -0.3874977810814163)
c : (0.4762546608215495, -0.5027003666609191, -0.9462702362135886)
d : (1.0359937569662543, 0.20224374523034738, -0.5106736838357188)
e : (1.0230123814776029, 0.307383143402044, 0.4836988757161117)
f : (0.45029148975467304, -0.2924180568179887, 1.0424721257882053)
g : (-0.10944707116299812, -0.997358709577812, 0.6068747551688862)
h : (-0.9094054351014828, -0.7372999161800771, 0.06610636023633815)
i : (-0.3376417190361616, -0.13788964934536008, -0.4940701491826226)
j : (0.236034423700416, 0.4623021632291133, -1.0514439507503563)
k : (0.22362339649149215, 0.5688921126903226, -0.057216744699174926)
l : (0.21007488818945885, 0.672587463030812, 0.9373014373359293)
m : (-0.35047427913383666, -0.0324315847098553, 0.5028609623423794)
n : (-1.1496245045538998, 0.2277041021133973, -0.03906859723472067)
o : (-0.5769046560901313, 0.8275063667800511, -0.5978396612020269)
p : (-0.589884877494203, 0.9326466019466428, 0.3965316761806731)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['l', 'm', 'p'], ['i', 'n', 'h'], ['m', 'n', 'h'], ['i', 'b', 'h'], ['a', 'g', 'f'], ['d', 'a', 'c'], ['l', 'e', 'f'], ['m', 'n', 'p'], ['l', 'k', 'p'], ['i', 'j', 'c'], ['b', 'h', 'g'], ['o', 'j', 'i'], ['l', 'e', 'k'], ['p', 'k', 'o'], ['l', 'm', 'f'], ['d', 'k', 'j'], ['d', 'e', 'a'], ['d', 'j', 'c'], ['b', 'a', 'g'], ['d', 'e', 'k'], ['k', 'j', 'o'], ['o', 'n', 'i'], ['m', 'h', 'g'], ['c', 'b', 'i'], ['p', 'o', 'n'], ['b', 'a', 'c'], ['e', 'a', 'f'], ['m', 'g', 'f']]
Coordinate Data:
i : [598262416352303521 / 625000000000000000, 34222666811696654981 / 50000000000000000000, 46492375098157387311 / 50000000000000000000]
e : [-2521463964687992361 / 6250000000000000000, 23918054348652902837 / 100000000000000000000, -4792152293558659737 / 100000000000000000000]
l : [20475162946903258877 / 50000000000000000000, -1575297201777986971 / 12500000000000000000, -50152408455540416059 / 100000000000000000000]
m : [97005242626136065721 / 100000000000000000000, 57899527159842829307 / 100000000000000000000, -3354180478092714887 / 50000000000000000000]
g : [72902521829052214613 / 100000000000000000000, 15439223964663850407 / 10000000000000000000, -684389609553444701 / 4000000000000000000]
k : [9898868765900796081 / 25000000000000000000, -279105322521868839 / 12500000000000000000, 49299409747970001937 / 100000000000000000000]
b : [716043681845901499 / 1000000000000000000, 82453260800950538897 / 50000000000000000000, 41163756693097067443 / 50000000000000000000]
f : [4232166434321274547 / 25000000000000000000, 41949087185328090237 / 50000000000000000000, -60669477300768005631 / 100000000000000000000]
c : [14332348630597452747 / 100000000000000000000, 52463202677474608569 / 50000000000000000000, 138204758899411371661 / 100000000000000000000]
o : [1495603504022069093 / 1250000000000000000, -28094267989147809653 / 100000000000000000000, 51680850699127599283 / 50000000000000000000]
j : [38354372342710802393 / 100000000000000000000, 4213076182972986283 / 50000000000000000000, 148722130353088137383 / 100000000000000000000]
d : [-8328312196774606863 / 20000000000000000000, 17215997082911281841 / 50000000000000000000, 47322551830812191397 / 50000000000000000000]
a : [310030134475759309 / 2000000000000000000, 47261478644442759521 / 50000000000000000000, 38754274134942220727 / 100000000000000000000]
p : [60473151231086350503 / 50000000000000000000, -38608291505806977323 / 100000000000000000000, 3924567659985198537 / 100000000000000000000]
n : [35384053033628476707 / 20000000000000000000, 15942979238758787397 / 50000000000000000000, 47484595001524575727 / 100000000000000000000]
h : [7644917911145033807 / 5000000000000000000, 128386360306865014719 / 100000000000000000000, 36967099254418696201 / 100000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 16
|E| = 42
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 125303027317710553092965541181686818546967375800812974649038391659130890596363201841113156933590100139154356964565125681 / 250000128409095413440591459155075762997778276292341843666966863674115683778328235000000000000000000000000000000000000000
Collision distance in [70796317 / 100000000, 35398159 / 50000000] ~ [0.70796, 0.70796]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [23 / 5000, 3 / 625] ~ [0.0046, 0.0048]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 405490538330511064566261959455538105690176547437043245497523811477943 / 1562500000000000000000000000000000000000000000000000000000000000000000000000000
rho in [32218873 / 2000000000000, 32238873 / 2000000000000] ~ [2e-05, 2e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [529 / 2592296280, 144 / 648074069] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)