show/hide visualization coordinates
a : (0.3669257613869808, 0.8947778916670243, -0.2608484597326903)
b : (0.6505435151643006, 0.853065290042201, 0.6971812037237956)
c : (0.9857172198149025, 0.17179620321114564, 0.046388593783636134)
d : (1.0220357616885982, 0.4922026980809907, -0.9001950793183795)
e : (0.04498945283648953, 0.30462917338998863, -1.0011737239226932)
f : (-0.6101205713742488, 0.7072046099181616, -0.36182727635844636)
g : (-0.27081216741007075, 1.1621839068284068, 0.46149747657578466)
h : (-0.12068423989230298, 0.21959355099158417, 0.7598053825517849)
i : (0.800965134562839, -0.09005598862439362, 0.9936475769667644)
j : (0.6274623602995828, -0.738759073288666, 0.25264704245804326)
k : (0.6637808465611563, -0.418352551642703, -0.6939366201261266)
l : (-0.31326545947319306, -0.6059260802960778, -0.7949152779969348)
m : (-0.9320568471036943, 0.11705565759912251, -1.1021523766223233)
n : (-0.9683753185332022, -0.20335066676968094, -0.15556865059643504)
o : (-1.0417481398996518, 0.5281787355377615, 0.5222813647173036)
p : (-0.8913277193656357, -0.41494273710594426, 0.8187477514981102)
q : (0.03002845990885944, -0.7240603724620985, 1.0544308031074516)
r : (-0.3495839811493505, -0.926332444812869, 0.15166843710369815)
s : (0.30552593197764194, -1.3289078022639527, -0.48767816781234263)
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'], ['r', 'n', 'l'], ['h', 'o', 'g'], ['o', 'f', 'g'], ['e', 'a', 'f'], ['i', 'c', 'b'], ['r', 'q', 'p'], ['o', 'n', 'p'], ['e', 'm', 'l'], ['r', 'q', 'j'], ['i', 'h', 'q'], ['i', 'j', 'q'], ['r', 'n', 'p'], ['n', 'f', 'm'], ['s', 'k', 'l'], ['q', 'h', 'p'], ['d', 'a', 'c'], ['r', 's', 'j'], ['e', 'd', 'a'], ['a', 'g', 'b'], ['a', 'c', 'b'], ['a', 'f', 'g'], ['i', 'c', 'j'], ['e', 'k', 'l'], ['e', 'f', 'm'], ['d', 'c', 'k'], ['k', 'c', 'j'], ['i', 'h', 'b'], ['r', 's', 'l'], ['e', 'd', 'k'], ['n', 'o', 'f'], ['s', 'k', 'j'], ['m', 'n', 'l'], ['h', 'o', 'p']]
Coordinate Data:
n : [-51367158246286742667 / 100000000000000000000, 1453451524150905423 / 5000000000000000000, 18787874840555570269 / 50000000000000000000]
l : [14143827659714163989 / 100000000000000000000, -1118851086962157551 / 10000000000000000000, -823716033091838501 / 3125000000000000000]
m : [-47735311103335950961 / 100000000000000000000, 61109662919898457093 / 100000000000000000000, -2283304916859107627 / 4000000000000000000]
e : [24984659445341212217 / 50000000000000000000, 79867014498985062833 / 100000000000000000000, -23492378825757339319 / 50000000000000000000]
r : [210239509841968427 / 2000000000000000000, -43229147321300698951 / 100000000000000000000, 68299458451124461347 / 100000000000000000000]
i : [125566887063317381873 / 100000000000000000000, 20199249148773421341 / 50000000000000000000, 152497372437431094831 / 100000000000000000000]
j : [21643321927398350571 / 20000000000000000000, -24471810168880395731 / 100000000000000000000, 39198659493279483801 / 50000000000000000000]
d : [147673949775893308729 / 100000000000000000000, 9862436696808527991 / 10000000000000000000, -18443446595541652997 / 50000000000000000000]
h : [16700974808901585849 / 50000000000000000000, 71363452259144619021 / 100000000000000000000, 64556576497966565569 / 50000000000000000000]
s : [76022966804797668331 / 100000000000000000000, -4174334153320452857 / 5000000000000000000, 4364797959520382291 / 100000000000000000000]
o : [-58704440382931697363 / 100000000000000000000, 51110985356881174711 / 50000000000000000000, 10536075121248500443 / 10000000000000000000]
p : [-8732479665906018797 / 20000000000000000000, 1977455862347944339 / 25000000000000000000, 27001477978113133927 / 20000000000000000000]
f : [-3108336706078283161 / 20000000000000000000, 120124558151802369707 / 100000000000000000000, 16949887104910008369 / 100000000000000000000]
q : [3029576224869963413 / 6250000000000000000, -11500970043111825873 / 50000000000000000000, 79287847525749907253 / 50000000000000000000]
b : [55262362561731774623 / 50000000000000000000, 33677656541051576733 / 25000000000000000000, 61425367556567100209 / 50000000000000000000]
c : [72021047794261865039 / 50000000000000000000, 3329185874055038453 / 5000000000000000000, 28885737059559129477 / 50000000000000000000]
a : [657303597965852371 / 800000000000000000, 138881886326688634033 / 100000000000000000000, 27047768767485617793 / 100000000000000000000]
g : [3677831373205278679 / 20000000000000000000, 165622487842826892899 / 100000000000000000000, 99282362398333112229 / 100000000000000000000]
k : [27962114565787278103 / 25000000000000000000, 7568841995715904953 / 100000000000000000000, -16261047271858013123 / 100000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 2857555728378630908908572945375785906809128908880598445404867814433566687778209520727124305288785965638454887357353267 / 4504222254592525202831788921231499829649082055465931388400451687569743750658820000000000000000000000000000000000000000
Collision distance in [15930061 / 20000000, 39825153 / 50000000] ~ [0.7965, 0.7965]
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 = 144655626570090352851888441241847501443053001861048800434590913071297 / 2500000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [190168101 / 25000000000000, 190418101 / 25000000000000] ~ [1e-05, 1e-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)