show/hide visualization coordinates
a : (0.0544662347556748, -0.9782762227391919, -0.14289451576119516)
b : (0.79778903573579, -0.32456726902403643, -0.28479808225314895)
c : (0.43650190384240284, -0.479001215913647, 0.6347785632680081)
d : (-0.30681471267843097, -1.132715849696914, 0.776682646667461)
e : (-0.48754248402964717, -0.26852899156390764, 0.30708469495869717)
f : (-0.12615313916384258, -0.11404661559345752, -0.6124457156441236)
g : (0.4157556774946557, -0.8238460985149874, -1.062468447893465)
h : (1.1590742044032292, -0.17013363016931493, -1.2043754107563114)
i : (0.6198891487077742, 0.5409218643761411, -0.7530675898518322)
j : (0.26035699375016763, 0.3872939899001675, 0.1673330374203037)
k : (-0.10268386804134555, 0.23205400423930822, 1.086083513930788)
l : (0.07521461815668706, -0.6334366903728571, 1.5543547543595417)
m : (-0.8459996857408143, -0.42166245635376054, 1.2279891465700576)
n : (-1.0238991740911427, 0.44382774369864875, 0.7597183281215829)
o : (-0.6626078177015321, 0.5982579622297, -0.15985633233302865)
p : (-0.3013263173486572, 0.7526958365146017, -1.0794313285038033)
q : (0.2378585484622906, 0.041641820447986144, -1.5307385114849024)
r : (0.08070369629995644, 1.2519785281452562, -0.3017627052871974)
s : (-0.2805828628132161, 1.0975432903902653, 0.6178139544725678)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'g', 'b'], ['c', 'j', 'b'], ['e', 'a', 'f'], ['i', 'h', 'q'], ['e', 'n', 'm'], ['e', 'o', 'n'], ['s', 'n', 'k'], ['i', 'r', 'j'], ['d', 'a', 'c'], ['s', 'o', 'n'], ['i', 'r', 'p'], ['r', 's', 'j'], ['e', 'd', 'a'], ['a', 'g', 'b'], ['n', 'k', 'm'], ['d', 'c', 'l'], ['d', 'm', 'l'], ['l', 'k', 'm'], ['a', 'c', 'b'], ['o', 'f', 'p'], ['a', 'f', 'g'], ['e', 'd', 'm'], ['k', 'c', 'j'], ['i', 'j', 'b'], ['c', 'k', 'l'], ['i', 'h', 'b'], ['r', 's', 'o'], ['r', 'o', 'p'], ['e', 'o', 'f'], ['h', 'g', 'q'], ['s', 'k', 'j'], ['f', 'q', 'g'], ['i', 'p', 'q'], ['q', 'f', 'p']]
Coordinate Data:
n : [-13064746156461470557 / 25000000000000000000, 95563181015474324661 / 100000000000000000000, 64173108735439593681 / 50000000000000000000]
l : [57652394598937096737 / 100000000000000000000, -6081631195838127677 / 50000000000000000000, 41561972018935012057 / 20000000000000000000]
m : [-34469035790813043433 / 100000000000000000000, 9014161010233401017 / 100000000000000000000, 17517329931572666163 / 10000000000000000000]
e : [275336876060734097 / 20000000000000000000, 24327507489218689659 / 100000000000000000000, 83082854154590622229 / 100000000000000000000]
r : [58201302413264029219 / 100000000000000000000, 176378259460135083857 / 100000000000000000000, 22198114130001166031 / 100000000000000000000]
i : [56059923827022910911 / 50000000000000000000, 105272593083223566811 / 100000000000000000000, -5733093581615578629 / 25000000000000000000]
d : [9724730757712646141 / 50000000000000000000, -15522794581020488443 / 25000000000000000000, 130042649325467005627 / 100000000000000000000]
h : [20754794152948912899 / 12500000000000000000, 2135440226792372561 / 6250000000000000000, -6806315641691023233 / 10000000000000000000]
j : [76166632158285157341 / 100000000000000000000, 89909805635626205881 / 100000000000000000000, 34553844200375639319 / 50000000000000000000]
s : [137954040637167349 / 625000000000000000, 4023368392115899721 / 2500000000000000000, 2853894502649441983 / 2500000000000000000]
o : [-16129848986884819969 / 100000000000000000000, 27751550717144863819 / 25000000000000000000, 7277750285083608373 / 20000000000000000000]
p : [9999150524201333137 / 50000000000000000000, 63224995148534812337 / 50000000000000000000, -55568748191659411343 / 100000000000000000000]
f : [18757809433442066801 / 50000000000000000000, 497196813578296267 / 1250000000000000000, -2217546726422865049 / 25000000000000000000]
q : [1847919690737436133 / 2500000000000000000, 6918073586301008151 / 12500000000000000000, -25174866622442334491 / 25000000000000000000]
b : [129909836356847381701 / 100000000000000000000, 18723679743205811493 / 100000000000000000000, 2986822054175751573 / 12500000000000000000]
c : [1172264039593858393 / 1250000000000000000, 3280285054244752571 / 100000000000000000000, 57926120492760862023 / 50000000000000000000]
a : [11115511251767174293 / 20000000000000000000, -46647215628309738457 / 100000000000000000000, 19042466541300695001 / 50000000000000000000]
g : [9170650053273396049 / 10000000000000000000, -31204203205889276069 / 100000000000000000000, -26936230065312785797 / 50000000000000000000]
k : [7972509195826766391 / 20000000000000000000, 37192903534770137647 / 50000000000000000000, 32196547210359944819 / 20000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 500854750937702330367584853135062918806326066648467072921124368102620954496118908177567253899774424902303455315491925801 / 1000002531249122778290952629832670862252655532792870353383390447743290384997346570000000000000000000000000000000000000000
Collision distance in [35385501 / 50000000, 70771003 / 100000000] ~ [0.70771, 0.70771]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [67 / 10000, 69 / 10000] ~ [0.0067, 0.0069]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 48107111150725583496192068927034625401049303755257439078670663408790563 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [219333333 / 10000000000000, 219433333 / 10000000000000] ~ [2e-05, 2e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [4489 / 11426285488, 1587 / 3808761824] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)