show/hide visualization coordinates
a : (-0.7071881679425185, -0.05308409682599197, -0.4163292694200822)
b : (-0.7056856905891711, 0.9390013500974934, -0.5419003016358936)
c : (0.01578967840875073, 0.3818733298866573, -0.9530928541786399)
d : (0.015373188156811102, -0.6100038484590713, -0.8259005289235397)
e : (-0.7065204816253159, -1.044752647416227, -0.2875120431043713)
f : (-1.4279950749519423, -0.48762712552478876, 0.12368054239280057)
g : (-1.4275785846987235, 0.5042498950969597, -0.0035129549643403424)
h : (-0.4954928611966915, 0.5513997272855509, 0.3556442639806272)
i : (0.22677487897131313, 0.9845667904803801, -0.18351775202019993)
j : (0.8782010404421743, 0.8877938884781531, -0.9360331702818132)
k : (0.8777848651747164, -0.1040838843714948, -0.8088391883704023)
l : (0.8773681947044986, -1.0959616402048542, -0.6816450857501639)
m : (0.22594189971915457, -0.9991882361707298, 0.0708689891874259)
n : (-0.495948748683197, -0.44353108104084465, 0.48332759465131997)
o : (-1.2170096734517135, 0.11506554180575718, 0.8932556734639356)
p : (-0.2845495491190521, 0.1606307742121444, 1.251637206319646)
q : (0.43734448085375627, 0.5953826182096313, 0.7132516241656615)
r : (1.0887707726638953, 0.49860888238540163, -0.03926373634879954)
s : (1.0883539262142083, -0.4932688683213395, 0.0879304144027982)
t : (0.4369267518183068, -0.39649529300506386, 0.8404445438221844)
u : (1.29933915513074, 0.1094239234022778, 0.8575060326118479)
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'], ['i', 'b', 'c'], ['c', 'k', 'd'], ['i', 'q', 'r'], ['f', 'o', 'n'], ['q', 'h', 'p'], ['f', 'a', 'g'], ['m', 'l', 'd'], ['c', 'd', 'a'], ['b', 'a', 'g'], ['o', 'n', 'p'], ['f', 'a', 'e'], ['f', 'n', 'e'], ['m', 't', 's'], ['m', 't', 'n'], ['s', 'l', 'm'], ['s', 'k', 'r'], ['m', 'n', 'e'], ['i', 'j', 'r'], ['m', 'd', 'e'], ['s', 'r', 'u'], ['i', 'c', 'j'], ['l', 'k', 'd'], ['k', 'r', 'j'], ['t', 'q', 'u'], ['f', 'o', 'g'], ['t', 'q', 'p'], ['i', 'q', 'h'], ['b', 'c', 'a'], ['o', 'g', 'h'], ['s', 'l', 'k'], ['o', 'h', 'p'], ['t', 'n', 'p'], ['d', 'a', 'e'], ['b', 'g', 'h'], ['q', 'r', 'u'], ['i', 'b', 'h'], ['c', 'k', 'j']]
Coordinate Data:
f : [47385406080917837049 / 25000000000000000000, 19063136496315146321 / 20000000000000000000, 1248099136734717329 / 3125000000000000000]
n : [96336991696796812267 / 100000000000000000000, 90906078033181326189 / 100000000000000000000, 3974467149659018083 / 100000000000000000000]
h : [19258280589629252691 / 20000000000000000000, -858700279945822833 / 10000000000000000000, 16742800216728291519 / 100000000000000000000]
q : [3007668743101486503 / 100000000000000000000, -3246322972966567167 / 25000000000000000000, -760717432071005557 / 4000000000000000000]
d : [5650599751599500831 / 12500000000000000000, 107553354775003978233 / 100000000000000000000, 134897279507144978231 / 100000000000000000000]
g : [189499975298349446459 / 100000000000000000000, -3872019580599111357 / 100000000000000000000, 13164630527806261701 / 25000000000000000000]
e : [11739416499100869541 / 10000000000000000000, 151028234670719553037 / 100000000000000000000, 81058430925228144797 / 100000000000000000000]
l : [-40994702641972740547 / 100000000000000000000, 78074566974791140541 / 50000000000000000000, 120471735189807399671 / 100000000000000000000]
m : [24147926856561657689 / 100000000000000000000, 1171774348369358679 / 800000000000000000, 22610163848024212593 / 50000000000000000000]
t : [3049441646646435713 / 100000000000000000000, 2693828100925101397 / 3125000000000000000, -7934306941856854011 / 25000000000000000000]
j : [-20538993607870159853 / 50000000000000000000, -42226418918718445999 / 100000000000000000000, 145910543642972342789 / 100000000000000000000]
o : [8422154208682423433 / 5000000000000000000, 3504641574852114111 / 10000000000000000000, -462729259145031903 / 1250000000000000000]
i : [6016157232836450549 / 25000000000000000000, -12975927279735288187 / 25000000000000000000, 14131800363362201217 / 20000000000000000000]
u : [-83191798684596893567 / 100000000000000000000, 17805288794434539547 / 50000000000000000000, -2090211040399610823 / 6250000000000000000]
a : [1174609336227289659 / 1000000000000000000, 810334056432750921 / 1562500000000000000, 46970076778399615853 / 50000000000000000000]
b : [117310685887394227359 / 100000000000000000000, -47347165080652479873 / 100000000000000000000, 106497256778380375531 / 100000000000000000000]
k : [-20518184844497261793 / 50000000000000000000, 28480679183123168881 / 50000000000000000000, 133191145451831244479 / 100000000000000000000]
p : [75197071740382328217 / 100000000000000000000, 15244946253941211817 / 50000000000000000000, -9107061752146696563 / 12500000000000000000]
s : [-3104663789647185591 / 5000000000000000000, 95879856761230803407 / 100000000000000000000, 10878546293627798227 / 25000000000000000000]
c : [45163148987602041431 / 100000000000000000000, 8365636940431131763 / 100000000000000000000, 147616512032655004123 / 100000000000000000000]
r : [-62134960437912422643 / 100000000000000000000, -1653959154721651417 / 50000000000000000000, 28116800124835486057 / 50000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 21
|E| = 57
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 2229030868570602813635555187783329315126638431232565183339337501193489999107569568754780474966416662743474871973025681 / 4444423182197266746180600760576446486562765873864347089495411837097088081060700000000000000000000000000000000000000000
Collision distance in [141638179142702498430471382119 / 200000000000000000000000000000, 177047723928378123038089227649 / 250000000000000000000000000000] ~ [0.70819, 0.70819]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [3 / 500, 31 / 5000] ~ [0.006, 0.0062]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 650360139963675859613475385193180581191347148675114824872013572080157 / 4000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [12751079757844782805229817 / 1000000000000000000000000000000, 6375539878922391402614909 / 500000000000000000000000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [2250000000000000000000000 / 7549834435270749697236684806947, 1201250000000000000000000 / 3774917217635374848618342403473] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)