show/hide visualization coordinates
a : (-0.7243423993677772, 0.3233132714413331, 0.41636627105466767)
b : (-0.6894229071369603, -0.5125541332431565, -0.13145533006109228)
c : (-0.17184457895819105, -0.4521270169704573, 0.7220433834952156)
d : (-0.20676771171562147, 0.38373770807099833, 1.2698661034842553)
e : (0.2735560057073896, 0.38366372375578955, 0.3927744875353672)
f : (-0.24401600261629652, 0.3230614311412223, -0.46072351494404545)
g : (-1.2419271481280076, 0.2628833978527051, -0.4371278653265848)
h : (-1.2070026846783697, -0.5729798564115318, -0.9849534856659181)
i : (-0.20891087575141887, -0.5158859552212302, -1.0084350881599606)
j : (0.308784115258122, -0.45744822634378324, -0.15486627966274952)
k : (0.82624741416747, -0.39503220698545893, 0.6985618593997176)
l : (0.34573412012482874, -0.39169894618649503, 1.5755429711000952)
m : (0.3108083971917299, 0.44416541355169875, 2.1233668160557793)
n : (0.7913218920679302, 0.4408312950268473, 1.2463850377595285)
o : (1.2718332945900226, 0.4374996980175383, 0.36940558345892144)
p : (0.7542510473574364, 0.3770702449317075, -0.4840893205124344)
q : (0.23667749405249858, 0.31664620722844217, -1.337590652301302)
r : (-0.7614141058745739, 0.259551839511322, -1.314108762916951)
s : (-1.7595067135231086, 0.20245788785201163, -1.2906258258735857)
t : (0.7891815364906734, -0.4587915000524946, -1.0319168501237346)
u : (1.3067598107422256, -0.3983642769670086, -0.17841953779518932)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['r', 'f', 'g'], ['l', 'n', 'm'], ['u', 'o', 'k'], ['u', 'p', 'o'], ['n', 'o', 'e'], ['c', 'j', 'b'], ['d', 'l', 'm'], ['h', 'r', 'i'], ['c', 'a', 'b'], ['q', 'p', 'f'], ['d', 'm', 'n'], ['h', 'b', 'g'], ['r', 'q', 'i'], ['u', 't', 'p'], ['j', 'b', 'i'], ['u', 't', 'j'], ['r', 's', 'g'], ['d', 'c', 'a'], ['h', 'r', 's'], ['h', 's', 'g'], ['t', 'j', 'i'], ['h', 'b', 'i'], ['c', 'j', 'k'], ['p', 'f', 'e'], ['l', 'n', 'k'], ['l', 'c', 'k'], ['a', 'b', 'g'], ['t', 'q', 'i'], ['d', 'l', 'c'], ['r', 'q', 'f'], ['a', 'f', 'g'], ['q', 't', 'p'], ['a', 'f', 'e'], ['n', 'o', 'k'], ['p', 'o', 'e'], ['u', 'j', 'k'], ['d', 'a', 'e'], ['d', 'n', 'e']]
Coordinate Data:
l : [5507023504779822839 / 50000000000000000000, 17157521231288596429 / 20000000000000000000, -5941458031800307791 / 5000000000000000000]
k : [-4629660299338060549 / 12500000000000000000, 86120932236339380669 / 100000000000000000000, -31131049465968380597 / 100000000000000000000]
a : [118021698958820243247 / 100000000000000000000, 14286384393660172299 / 100000000000000000000, -582298126292677813 / 20000000000000000000]
r : [24345773921899982303 / 20000000000000000000, 2066252758666128479 / 10000000000000000000, 170136012765698469841 / 100000000000000000000]
o : [-81595870436959722609 / 100000000000000000000, 358467717004956779 / 12500000000000000000, 223072266013904297 / 12500000000000000000]
i : [33239273298592202583 / 50000000000000000000, 1534473547811195289 / 1562500000000000000, 69784322644999719881 / 50000000000000000000]
u : [-42544261026090020609 / 50000000000000000000, 86454139234494345513 / 100000000000000000000, 3535443140845144599 / 6250000000000000000]
c : [12554383383572325507 / 20000000000000000000, 91830413234839219913 / 100000000000000000000, -33479201875518176439 / 100000000000000000000]
t : [-33330694627024817939 / 100000000000000000000, 92496861543042935323 / 100000000000000000000, 35479205371594210357 / 25000000000000000000]
m : [14506619302869529609 / 100000000000000000000, 2201170182623609679 / 100000000000000000000, -34722309026314903973 / 20000000000000000000]
b : [57264874867869279919 / 50000000000000000000, 24468281215527282577 / 25000000000000000000, 51870669480112610999 / 100000000000000000000]
n : [-1677236509237525169 / 5000000000000000000, 2534582035108750281 / 100000000000000000000, -17182673460389894431 / 20000000000000000000]
e : [9115929225651779567 / 50000000000000000000, 4125669581107262733 / 50000000000000000000, -55231227953334247 / 10000000000000000000]
j : [14709047496230324039 / 100000000000000000000, 92362534172171809821 / 100000000000000000000, 54211764440278332703 / 100000000000000000000]
d : [33132115096802335089 / 50000000000000000000, 8243940730693651333 / 100000000000000000000, -44130736937211073151 / 50000000000000000000]
p : [-5967529142740223729 / 20000000000000000000, 8910687044622730687 / 100000000000000000000, 17426813705049364911 / 20000000000000000000]
g : [169780173834843301187 / 100000000000000000000, 5082342938130742949 / 25000000000000000000, 2060948075166546637 / 2500000000000000000]
h : [41571931872469875339 / 25000000000000000000, 51957848589473334461 / 50000000000000000000, 137220485040595192311 / 100000000000000000000]
f : [69989059283672167843 / 100000000000000000000, 2862313684734250071 / 20000000000000000000, 42398743984203965133 / 50000000000000000000]
s : [110769065187176680109 / 50000000000000000000, 26371922752592317667 / 100000000000000000000, 167787719061361944579 / 100000000000000000000]
q : [21919709616792661653 / 100000000000000000000, 14953090814949265727 / 100000000000000000000, 8624210085206678851 / 5000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 21
|E| = 57
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 10416634936785458574977069341256419590766900065530655126011403227175814758885933221541311095336450846592154164088050307 / 20833333595273116507283519751164346537524037491782610380268997825270655163813404375000000000000000000000000000000000000
Collision distance in [353552849896294303560103367409 / 500000000000000000000000000000, 707105699792588607120206734819 / 1000000000000000000000000000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [4 / 625, 33 / 5000] ~ [0.0064, 0.0066]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 38056374694627866616879139927561199961462375309522706200714846713911959 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [1950804313472467863685897 / 100000000000000000000000000000, 19508043134724678636858971 / 1000000000000000000000000000000] ~ [2e-05, 2e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [2560000000000000000000000 / 7549834435270749697236684806947, 453750000000000000000000 / 1258305739211791616206114134491] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)