show/hide visualization coordinates
a : (0.22460185328500004, -1.270127683455, -0.32643126472499995)
b : (-0.28764907961499997, -0.6013337704549999, 0.21237638937499997)
c : (-0.405664334515, -0.6399337922549999, -0.7798848873249999)
d : (0.539884793885, -0.3637561856549999, -0.6076560424249999)
e : (1.162338305485, -0.9837026376549999, -0.129934343425)
f : (0.8455734489850001, -1.888198923055, 0.15562912587500005)
g : (0.49949031908499997, -1.0695243581549998, 0.613884975975)
h : (0.12939161768500002, -0.24946996215499992, 1.050391258375)
i : (-0.724129187015, 0.1468388584450001, 0.712099149975)
j : (-0.999017652815, -0.053764466854999915, -0.22821709102499999)
k : (-0.181224377015, 0.32711028214500004, -0.659666489925)
l : (0.7310659522849999, 0.5798666894450001, -0.33742348622499996)
m : (1.479087474985, -0.07919984835499994, -0.41549461432499996)
n : (0.8125474577849999, -0.16477716745499993, 0.325046355275)
o : (0.151111488385, 0.5696365719450002, 0.47716117137499997)
p : (-0.682720354115, 1.121453645445, 0.492073409975)
q : (-1.5201044709149998, 0.6041451010450002, 0.31549563517500007)
r : (-0.957608820415, 0.9208503198450001, -0.448242832825)
s : (-0.025903952915000028, 1.2280218383450001, -0.254408629825)
t : (-0.791070482515, 1.865865488845, -0.166797789325)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'j', 'b'], ['o', 'h', 'i'], ['g', 'e', 'n'], ['k', 'j', 'c'], ['o', 'l', 'n'], ['d', 'm', 'l'], ['d', 'c', 'a'], ['b', 'a', 'g'], ['p', 't', 'r'], ['d', 'e', 'a'], ['m', 'e', 'n'], ['p', 't', 's'], ['t', 'r', 's'], ['f', 'a', 'g'], ['f', 'e', 'a'], ['o', 's', 'p'], ['p', 'o', 'i'], ['d', 'k', 'c'], ['o', 'l', 's'], ['c', 'a', 'b'], ['j', 'c', 'b'], ['k', 'r', 's'], ['q', 'j', 'i'], ['d', 'm', 'e'], ['o', 'h', 'n'], ['p', 'q', 'r'], ['r', 'q', 'j'], ['p', 'q', 'i'], ['h', 'n', 'g'], ['d', 'l', 'k'], ['k', 'l', 's'], ['i', 'h', 'b'], ['f', 'e', 'g'], ['r', 'k', 'j'], ['m', 'l', 'n'], ['g', 'h', 'b']]
Coordinate Data:
d : [9076969103 / 10000000000, 21495021 / 200000000, -667185341 / 5000000000]
s : [683816327 / 2000000000, 1699253129 / 1000000000, 549525861 / 2500000000]
k : [932938697 / 5000000000, 498963483 / 625000000, -1854475157 / 10000000000]
r : [-18431147 / 31250000, 2784163221 / 2000000000, 129880707 / 5000000000]
n : [5901797871 / 5000000000, 191533827 / 625000000, 1598530659 / 2000000000]
j : [-1578013841 / 2500000000, 2087334119 / 5000000000, 153751177 / 625000000]
a : [5924139697 / 10000000000, -998620491 / 1250000000, 295575419 / 2000000000]
o : [324327253 / 625000000, 5204339313 / 5000000000, 594612591 / 625000000]
m : [9234497957 / 5000000000, 3920314423 / 10000000000, 587243599 / 10000000000]
b : [25050949 / 312500000, -650512399 / 5000000000, 1716488409 / 2500000000]
l : [10988780687 / 10000000000, 10510979801 / 10000000000, 4274859 / 31250000]
q : [-2304584709 / 2000000000, 10753763917 / 10000000000, 3948573047 / 5000000000]
f : [6066927827 / 5000000000, -3542419081 / 2500000000, 6298481001 / 10000000000]
i : [-1781585353 / 5000000000, 6180701491 / 10000000000, 5931590621 / 5000000000]
p : [-3149082377 / 10000000000, 15926849361 / 10000000000, 4831461921 / 5000000000]
g : [1734604871 / 2000000000, -239317227 / 400000000, 5440519751 / 5000000000]
e : [15301504219 / 10000000000, -512471347 / 1000000000, 860711577 / 2500000000]
t : [-4232583661 / 10000000000, 4674193559 / 2000000000, 3074211849 / 10000000000]
h : [4972037341 / 10000000000, 443522657 / 2000000000, 7623051163 / 5000000000]
c : [-378522181 / 10000000000, -210878127 / 1250000000, -3056659131 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 123975700328141428070438992897299323942237466178026592249369 / 249983741369094004577874780801875327309300000000000000000000
Collision distance in [550177 / 781250, 70422657 / 100000000] ~ [0.70423, 0.70423]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [3973 / 10000, 159 / 400] ~ [0.3973, 0.3975]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1085761523507843945112717 / 5000000000000000000000000000000000000000
rho in [29472177 / 2000000000000000, 49472177 / 2000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [15784729 / 11757550768, 1755625 / 1306394528] ~ [0.00134, 0.00134]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19783 / 100000000, 20367 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-19783 / 5878775376, 2263 / 653197264] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [17605664 / 111803399, 70422657 / 447213595] ~ [0.15747, 0.15747]
Success: LHS < CD / |V| ^ .5
Success: existence proven