show/hide visualization coordinates
a : (-0.49432614366527117, 0.0840353594603338, 0.6515780963962834)
b : (-0.9052505306622435, -0.785691619440589, 0.9249272202175401)
c : (0.04966739525674835, -0.5914213845469252, 1.1494017290927696)
d : (0.461097308290303, 0.27758350562272194, 0.8745311223429408)
e : (-0.08239257594343657, 0.9523191319526396, 0.37518231323566287)
f : (-1.0373101295705238, 0.7580504607792751, 0.1507069174265363)
g : (-1.448738846430337, -0.11095297924104236, 0.4255785742800408)
h : (-1.1704587953252101, -0.960077779051282, -0.023361725450510296)
i : (-0.2152403181761211, -0.7675653853302897, 0.20135263160987724)
j : (0.7393762448628216, -0.5715411159880541, 0.4255898864276304)
k : (1.150806052466744, 0.2974647856349606, 0.15071724228942562)
l : (0.8725261411590788, 1.1465892986202084, 0.5996579809101465)
m : (0.6073163565268956, 0.9722016812513551, -0.34863140553215305)
n : (-0.3476024945110493, 0.7779320480987804, -0.5731070990087077)
o : (-0.7603518541176818, -0.09084262532409121, -0.2994861393536133)
p : (-0.48075154193243164, -0.9401958097705614, -0.747174608636773)
q : (0.47416690535546857, -0.7459282622595209, -0.5226985844787897)
r : (1.4290864807716632, -0.5516595236541559, -0.29822363790196077)
s : (0.8855963218636731, 0.12307712405369609, -0.797572136695925)
t : (0.342106902052822, 0.797814174905435, -1.2969208882022412)
u : (-0.06932287827191175, -0.07119108577289496, -1.0220474889681797)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['s', 't', 'u'], ['f', 'o', 'n'], ['m', 'l', 'e'], ['o', 'n', 'u'], ['f', 'a', 'g'], ['i', 'q', 'p'], ['c', 'd', 'a'], ['b', 'a', 'g'], ['l', 'd', 'e'], ['q', 'r', 'j'], ['f', 'a', 'e'], ['o', 'p', 'u'], ['f', 'n', 'e'], ['s', 'k', 'm'], ['m', 't', 's'], ['m', 't', 'n'], ['s', 'k', 'r'], ['m', 'n', 'e'], ['i', 'q', 'j'], ['t', 'n', 'u'], ['c', 'd', 'j'], ['s', 'q', 'u'], ['q', 'p', 'u'], ['i', 'c', 'j'], ['l', 'k', 'd'], ['k', 'r', 'j'], ['s', 'q', 'r'], ['f', 'o', 'g'], ['b', 'c', 'a'], ['o', 'g', 'h'], ['m', 'l', 'k'], ['o', 'h', 'p'], ['d', 'a', 'e'], ['i', 'h', 'p'], ['b', 'g', 'h'], ['k', 'd', 'j'], ['i', 'b', 'h'], ['i', 'b', 'c']]
Coordinate Data:
f : [28682608551385792839 / 20000000000000000000, -675169808072103249 / 2500000000000000000, 27917366879167208737 / 100000000000000000000]
n : [37221139625490764779 / 50000000000000000000, -28994951054834667183 / 100000000000000000000, 100298768522691607827 / 100000000000000000000]
h : [9795494333274851349 / 6250000000000000000, 72403015830085778359 / 50000000000000000000, 9064846233374373653 / 20000000000000000000]
q : [-7734660735670259557 / 100000000000000000000, 123391079980995463171 / 100000000000000000000, 95257917069699808501 / 100000000000000000000]
d : [-6427701029153702269 / 100000000000000000000, 1314993949548198631 / 6250000000000000000, -8893010722494649591 / 20000000000000000000]
g : [184555914442910297343 / 100000000000000000000, 29946775839573803623 / 50000000000000000000, 43020119381675799 / 10000000000000000000]
e : [2995080462138765687 / 6250000000000000000, -232168297201102959 / 500000000000000000, 5469827298254555751 / 100000000000000000000]
l : [-5946323039503909661 / 12500000000000000000, -8232584513372184793 / 12500000000000000000, -16977739469193819747 / 100000000000000000000]
m : [-21049605852812968787 / 100000000000000000000, -3026369648130758613 / 6250000000000000000, 38925599587518072891 / 50000000000000000000]
t : [5471339594594391507 / 100000000000000000000, -30983163735500141717 / 100000000000000000000, 172680147442044960821 / 100000000000000000000]
j : [-34255594686405567963 / 100000000000000000000, 105952365353848771087 / 100000000000000000000, 26816873691112477 / 6250000000000000000]
o : [57858607605822386919 / 50000000000000000000, 3617657267965780591 / 6250000000000000000, 3646833627859108357 / 5000000000000000000]
i : [61206061617488705097 / 100000000000000000000, 12555479228807233821 / 10000000000000000000, 11426397730416558059 / 50000000000000000000]
u : [46614317627067767161 / 100000000000000000000, 27958681166166433591 / 50000000000000000000, 18149100939829852717 / 12500000000000000000]
a : [44557322083201856917 / 50000000000000000000, 20197358904504995073 / 50000000000000000000, -11084875508903746427 / 50000000000000000000]
b : [13020708286610094207 / 10000000000000000000, 127367415699102251773 / 100000000000000000000, -6188082924991647121 / 12500000000000000000]
k : [-75398575446797824377 / 100000000000000000000, 19051775191547312943 / 100000000000000000000, 2791633439287827697 / 10000000000000000000]
p : [43878591996559878079 / 50000000000000000000, 142817834732099492949 / 100000000000000000000, 117705519485498155353 / 100000000000000000000]
s : [-4887760238649070687 / 10000000000000000000, 18245270674836879253 / 50000000000000000000, 61372636145706667041 / 50000000000000000000]
c : [34715290274201761627 / 100000000000000000000, 107940392209735890233 / 100000000000000000000, -35976057143728062103 / 50000000000000000000]
r : [-51613309138644861431 / 50000000000000000000, 51982103060229475123 / 50000000000000000000, 18202605603004230371 / 25000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 21
|E| = 57
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 125361586351144086013407862623396721485570174072309671911171233372496184465174618195086667282808332735569820917571396569 / 249998766533726813459967885823803323488958371575425811127059069129732678327161340000000000000000000000000000000000000000
Collision distance in [708130510206559735584179907467 / 1000000000000000000000000000000, 177032627551639933896044976867 / 250000000000000000000000000000] ~ [0.70813, 0.70813]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [57 / 10000, 59 / 10000] ~ [0.0057, 0.0059]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 2870553177079815114926237727199188967267721752943853267984720513412001 / 20000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [2995075738336915952479159 / 250000000000000000000000000000, 11980302953347663809916637 / 1000000000000000000000000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [2030625000000000000000000 / 7549834435270749697236684806947, 1087812500000000000000000 / 3774917217635374848618342403473] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)