show/hide visualization coordinates
a : (0.38969179667876475, 0.1852447473608626, 0.14635243864877973)
b : (0.44918095786079704, -0.808685501598095, 0.23890054233320163)
c : (0.670920384872508, -0.3736181466488746, -0.6337648063960059)
d : (0.6097163762316933, 0.6201584919501278, -0.7268273077796918)
e : (0.32677205453186997, 1.1788673023729115, 0.052779530331415414)
f : (0.10503230530176211, 0.7438004158132819, 0.9254454983429368)
g : (0.16623724551258523, -0.24997525695164213, 1.0185065291671769)
h : (0.07712209338308518, -1.2452107760931228, 1.0580578025980267)
i : (-0.5215045098858377, -0.7130071158703706, 0.4593881414404232)
j : (-0.23012555664367007, -0.7843925545678951, -0.4945510707080429)
k : (0.20877661119263913, -0.8339802422956112, -1.3917165150079431)
l : (-0.13744075565005287, 0.04055142557362801, -1.0521142640181556)
m : (-0.3361347237289168, 0.9368791843762335, -0.6557382067130397)
n : (-0.6275142588140059, 1.0082636841799348, 0.2982017606481802)
o : (-0.7201992881171704, 0.18332143393270595, 0.8557658524518235)
p : (-0.4305307327260515, 0.11178290846592454, -0.0986859253390856)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['e', 'f', 'n'], ['l', 'm', 'p'], ['p', 'o', 'i'], ['i', 'b', 'h'], ['l', 'j', 'p'], ['a', 'g', 'f'], ['d', 'a', 'c'], ['b', 'j', 'c'], ['m', 'n', 'p'], ['m', 'e', 'n'], ['b', 'h', 'g'], ['i', 'o', 'g'], ['b', 'j', 'i'], ['d', 'e', 'a'], ['d', 'm', 'e'], ['o', 'g', 'f'], ['i', 'h', 'g'], ['o', 'n', 'f'], ['b', 'a', 'g'], ['l', 'd', 'c'], ['k', 'j', 'c'], ['l', 'k', 'j'], ['l', 'k', 'c'], ['p', 'o', 'n'], ['b', 'a', 'c'], ['d', 'm', 'l'], ['p', 'j', 'i'], ['e', 'a', 'f']]
Coordinate Data:
i : [6758219361555916153 / 50000000000000000000, -16943820281749063239 / 100000000000000000000, 11302908050027268301 / 12500000000000000000]
e : [4917204758244130131 / 5000000000000000000, 17224362154257914293 / 10000000000000000000, 49762403289317367833 / 100000000000000000000]
l : [51922814146690323997 / 100000000000000000000, 29206016931325396987 / 50000000000000000000, -7590872018204965011 / 12500000000000000000]
m : [8013354334700982541 / 25000000000000000000, 74022404871455669881 / 50000000000000000000, -21089370415128140921 / 100000000000000000000]
g : [82290614262954132827 / 100000000000000000000, 5871873122024755659 / 20000000000000000000, 36583775793223374863 / 25000000000000000000]
k : [8654455083095952149 / 10000000000000000000, -907535403883535287 / 3125000000000000000, -94687201244618476047 / 100000000000000000000]
f : [15234024048374364129 / 20000000000000000000, 5149477315464647083 / 4000000000000000000, 13702900009046950859 / 10000000000000000000]
b : [22116997099555061437 / 20000000000000000000, -13255829427260756271 / 50000000000000000000, 17093626122373998533 / 25000000000000000000]
o : [-254121564000857361 / 4000000000000000000, 9086129337319823241 / 12500000000000000000, 130061035501358169993 / 100000000000000000000]
c : [66379464099473204791 / 50000000000000000000, 6798030656160213 / 40000000000000000, -18892030383424754777 / 100000000000000000000]
j : [2132716702366430167 / 5000000000000000000, -24082364151501528601 / 100000000000000000000, -4970656814628460299 / 100000000000000000000]
d : [31659631833716235683 / 25000000000000000000, 29093185125075194561 / 25000000000000000000, -5639656104358670637 / 20000000000000000000]
a : [52318034689786039377 / 50000000000000000000, 291525464165497001 / 400000000000000000, 59119694121053797621 / 100000000000000000000]
p : [706681763721576751 / 3125000000000000000, 65535182151880444957 / 100000000000000000000, 17307928861133633389 / 50000000000000000000]
n : [2915463830295015413 / 100000000000000000000, 38795814930820364949 / 25000000000000000000, 37152313160496925063 / 50000000000000000000]
h : [36689549525002063251 / 50000000000000000000, -14032837260804858953 / 20000000000000000000, 150290230515978499327 / 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 = 2222222196712597587139074127506769187697004300107376070729585138957776429107300999595520912466694993728211934294620209 / 4444450341958601445614090539061289468424032012792581414153442294101187307049266400000000000000000000000000000000000000
Collision distance in [7071063 / 10000000, 70710631 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [61 / 10000, 63 / 10000] ~ [0.0061, 0.0063]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 10541478174957180029366620911043224742992243039819168697814085300609197 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [1026717 / 100000000000, 1027717 / 100000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [3721 / 10369185120, 3969 / 10369185104] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)