show/hide visualization coordinates
a : (-0.49675641115263164, -0.19690490866315796, -0.5757330546842104)
b : (0.06994251994736839, -0.747796887563158, -1.1884078045842106)
c : (-0.09411070025263163, -1.052405774963158, -0.25016478348421045)
d : (-0.6162246126526316, -0.4748622138631579, 0.3774023424157895)
e : (-0.8029098094526317, 0.46893669573684205, 0.10465290531578952)
f : (-0.5316768880526315, 0.7751558030368421, -0.8078505525842105)
g : (0.26196828854736837, 0.22651575283684205, -1.0707600978842104)
h : (0.6724076096473683, -0.44239467386315795, -0.45100336778421046)
i : (0.7770859278473683, -1.170582133863158, 0.22633367741578952)
j : (-0.08293200685263163, -1.2431575105631578, 0.7314098760157896)
k : (-0.05337988115263165, -0.3579433816631579, 1.1956540120157895)
l : (-0.8705900076526316, 0.20373107283684205, 1.0664664881157897)
m : (0.006479866647368382, 0.503254453436842, 0.6909213111157896)
n : (-0.14284318775263166, 1.213188378136842, 0.002665219415789566)
o : (-0.44036641585263164, 1.770354397036842, -0.7726063175842105)
p : (0.37430851564736833, 1.196043962736842, -0.8530568058842104)
q : (0.5442022565473683, 0.503269283036842, -0.1522006437842105)
r : (0.6750676566473683, -0.22146767056315791, 0.5242833508157896)
s : (0.7503272793473683, -0.9529346432631578, 1.2019942456157895)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['d', 'a', 'c'], ['h', 'i', 'c'], ['o', 'p', 'f'], ['d', 'a', 'e'], ['k', 's', 'r'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['o', 'n', 'f'], ['b', 'c', 'h'], ['n', 'p', 'q'], ['r', 'm', 'q'], ['r', 's', 'i'], ['d', 'k', 'j'], ['j', 's', 'i'], ['n', 'p', 'o'], ['b', 'g', 'a'], ['m', 'e', 'n'], ['d', 'j', 'c'], ['j', 'i', 'c'], ['l', 'k', 'm'], ['b', 'a', 'c'], ['h', 'g', 'q'], ['e', 'n', 'f'], ['r', 'h', 'i'], ['k', 's', 'j'], ['b', 'g', 'h'], ['g', 'p', 'f'], ['a', 'e', 'f'], ['m', 'n', 'q'], ['l', 'm', 'e'], ['k', 'r', 'm'], ['g', 'q', 'p'], ['r', 'h', 'q'], ['g', 'a', 'f']]
Coordinate Data:
d : [10863308161 / 10000000000, 298220817 / 312500000, 802350243 / 5000000000]
c : [5642169037 / 10000000000, 3063700351 / 2000000000, 1576074349 / 2000000000]
n : [766186739 / 1250000000, -229294993 / 312500000, 1338017929 / 2500000000]
s : [-2802210759 / 10000000000, 7161895219 / 5000000000, -3320609273 / 5000000000]
q : [-740960531 / 10000000000, -9529953 / 400000000, 1725182587 / 2500000000]
p : [478988439 / 5000000000, -3582997811 / 5000000000, 13909291969 / 10000000000]
i : [-767449311 / 2500000000, 128908323 / 78125000, 12169481 / 39062500]
m : [579532921 / 1250000000, -238100529 / 10000000000, -1530489201 / 10000000000]
a : [4834313073 / 5000000000, 1690873273 / 2500000000, 11136054457 / 10000000000]
b : [800327367 / 2000000000, 12272412881 / 10000000000, 4315700489 / 2500000000]
e : [12730160129 / 10000000000, 13134631 / 1250000000, 4332194857 / 10000000000]
r : [-512403633 / 2500000000, 7009120711 / 10000000000, 67945201 / 5000000000]
j : [5530382103 / 10000000000, 17226019111 / 10000000000, -38707497 / 200000000]
k : [2617430423 / 5000000000, 4186938911 / 5000000000, -657781621 / 1000000000]
l : [13406962111 / 10000000000, 2757133277 / 10000000000, -5285940971 / 10000000000]
h : [-1011507031 / 5000000000, 1152298843 / 1250000000, 2472189397 / 2500000000]
f : [2003566183 / 2000000000, -118284561 / 400000000, 3364307359 / 2500000000]
g : [2081379149 / 10000000000, 2529286477 / 10000000000, 16086324889 / 10000000000]
o : [9104726193 / 10000000000, -2581819993 / 2000000000, 6552393543 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 41666666663365185142658442985723354385078365086334273046043 / 83333333335548007476945449542789743053050000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5867 / 10000, 5869 / 10000] ~ [0.5867, 0.5869]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 12759578897727424813173 / 10000000000000000000000000000000000000000
rho in [56479153 / 50000000000000000, 556479153 / 50000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [34421689 / 11426285488, 34445161 / 11426285472] ~ [0.00301, 0.00301]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-1999 / 10000000, 20109 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-9995 / 2856571368, 6703 / 1904380912] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710678 / 435889895, 70710679 / 435889894] ~ [0.16222, 0.16222]
Success: LHS < CD / |V| ^ .5
Success: existence proven