show/hide visualization coordinates
a : (-0.6116767031858333, 0.551648209739112, 0.7559979335790548)
b : (-0.7355358023835498, -0.43992135133567734, 0.7179513788736236)
c : (-0.3445817296104494, -0.01585010807912579, 1.5348470329356176)
d : (0.35614544020905015, 0.422469876541669, 0.9719452839427221)
e : (-0.0035480933916730573, 1.3429622086761523, 0.8192573162477235)
f : (-0.36005181506086015, 1.0561584203593992, -0.06992622840463525)
g : (-0.4858363169426649, 0.06484585069777582, -0.10840380982932052)
h : (-0.607769119442059, -0.9269800319785084, -0.14601971907062294)
i : (-0.341032314939762, -1.3588120718357006, 0.7155902942342562)
j : (0.23228644242724994, -0.5690989260037621, 0.9338987881207768)
k : (0.48582863197940773, -0.06484466133790373, 0.10840139876537419)
l : (0.607770361787849, 0.9269796478469664, 0.14602069621176866)
m : (0.34103314632713666, 1.3588121979118153, -0.7155901547820421)
n : (-0.23228595421212173, 0.5690987295871769, -0.933898594182495)
o : (-0.3561446261155037, -0.4224697275469677, -0.9719458518707985)
p : (0.0035500205017018893, -1.342962674133498, -0.8192571329404472)
q : (0.36005317986453345, -1.0561584485028903, 0.06992687201792874)
r : (0.6116772931662556, -0.55164818263195, -0.7559976289199417)
s : (0.7355362176522336, 0.43992063476428345, -0.7179511899097797)
t : (0.34458174136905717, 0.015850407261634947, -1.5348466850187636)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['a', 'f', 'g'], ['f', 'g', 'n'], ['f', 'l', 'm'], ['b', 'j', 'i'], ['a', 'c', 'b'], ['s', 'l', 'm'], ['k', 's', 'l'], ['k', 'l', 'd'], ['k', 'q', 'j'], ['t', 's', 'n'], ['p', 'h', 'q'], ['h', 'q', 'i'], ['f', 'n', 'm'], ['k', 'j', 'd'], ['c', 'j', 'd'], ['q', 'j', 'i'], ['e', 'l', 'd'], ['t', 'r', 's'], ['n', 's', 'm'], ['b', 'c', 'j'], ['p', 'h', 'o'], ['h', 'g', 'o'], ['t', 'r', 'o'], ['a', 'e', 'd'], ['p', 'q', 'r'], ['k', 'q', 'r'], ['a', 'g', 'b'], ['a', 'c', 'd'], ['g', 'n', 'o'], ['p', 'r', 'o'], ['f', 'e', 'l'], ['b', 'h', 'g'], ['b', 'h', 'i'], ['t', 'n', 'o'], ['k', 'r', 's'], ['a', 'f', 'e']]
Coordinate Data:
b : [-5328295974096621517 / 20000000000000000000, -12545390054629783 / 4000000000000000000, 119122755483283981453 / 100000000000000000000]
k : [3819798542632505433 / 4000000000000000000, 37194034248411615087 / 100000000000000000000, 58167757472459035407 / 100000000000000000000]
m : [81015415000585528359 / 100000000000000000000, 44889930043345877861 / 25000000000000000000, -24231397882282596087 / 100000000000000000000]
a : [-3563892487677866493 / 25000000000000000000, 98843321356113192983 / 100000000000000000000, 61463705476913547173 / 50000000000000000000]
f : [681682428861615729 / 6250000000000000000, 74647171209070954603 / 50000000000000000000, 10083748688864523563 / 25000000000000000000]
j : [2191898269081151759 / 3125000000000000000, -13231392218174222897 / 100000000000000000000, 70358748203999645913 / 50000000000000000000]
t : [1017128431309719761 / 1250000000000000000, 45263541108365484187 / 100000000000000000000, -3317407840811086287 / 3125000000000000000]
l : [10768913654665676827 / 10000000000000000000, 136376465166898625961 / 100000000000000000000, 61929687217098478381 / 100000000000000000000]
g : [-835765663197310299 / 50000000000000000000, 1003261709039591339 / 2000000000000000000, 456090457662369541 / 1250000000000000000]
p : [47267102418042057869 / 100000000000000000000, -90617767031147785967 / 100000000000000000000, -34598095698123104023 / 100000000000000000000]
i : [12808868873895668373 / 100000000000000000000, -92202706801368073589 / 100000000000000000000, 118886647019347233277 / 100000000000000000000]
s : [24093144426619047067 / 20000000000000000000, 87670563858630335433 / 100000000000000000000, -4893500279011270307 / 20000000000000000000]
h : [-13864811576334032033 / 100000000000000000000, -4901950281564884977 / 10000000000000000000, 32725645688859323171 / 100000000000000000000]
n : [23683504946659695783 / 100000000000000000000, 3143386666903740237 / 3125000000000000000, -23031120911163941859 / 50000000000000000000]
q : [41458709177162605979 / 50000000000000000000, -3096867223404352367 / 5000000000000000000, 1086406095954289829 / 2000000000000000000]
o : [1412204719540187717 / 12500000000000000000, 715763813752609197 / 50000000000000000000, -24933483795579118101 / 50000000000000000000]
e : [181864418080877189 / 390625000000000000, 35594944249963441443 / 20000000000000000000, 12925334922069396463 / 10000000000000000000]
d : [82526644388776877717 / 100000000000000000000, 85925488036368894851 / 100000000000000000000, 72261072995096909489 / 50000000000000000000]
r : [108079829684497441081 / 100000000000000000000, -11486317880993010797 / 100000000000000000000, -7068036324018137833 / 25000000000000000000]
c : [12453927406826923497 / 100000000000000000000, 42093489574289410957 / 100000000000000000000, 50203080222370847807 / 25000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 31249909811775649667672055135796658328824632597456789251635399756446836662659164456941665472194973461755006472937389321 / 46874996434874922756462482116477031937170336913116250764258092360526965737183630000000000000000000000000000000000000000
Collision distance in [81649543 / 100000000, 10206193 / 12500000] ~ [0.8165, 0.8165]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [67 / 10000, 69 / 10000] ~ [0.0067, 0.0069]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1792126192958793707374779865789695925586271175160299086576264629353517 / 12500000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [29934313 / 2500000000000, 29959313 / 2500000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [4489 / 11757550768, 529 / 1306394528] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)