show/hide visualization coordinates
a : (-1.0238532871, -0.2155425765650001, -0.150730345925)
b : (-1.3774702135999999, -0.006418919465000061, 0.7609836251750001)
c : (-1.3638704838999998, 0.7020205293349999, 0.05534306907500003)
d : (-0.6148305734999999, 0.5809569003349999, -0.5960268798249999)
e : (-0.546164841, -0.32072476506500003, -1.022940444225)
f : (-0.23675330249999982, -0.8285802330650001, -0.21898315472499996)
g : (-0.4663406609999998, -0.4053232761650001, 0.657454631475)
h : (-0.5792728139999999, 0.588252119235, 0.664820915375)
i : (-0.6116832670999999, 1.360494716935, 0.03032037737500004)
j : (0.21095915680000016, 1.135201082035, -0.49169707492500003)
k : (0.28336881290000016, 0.177813694935, -0.771279321025)
l : (0.33938464690000014, -0.785108580465, -1.035178767725)
m : (0.5963390436000001, -1.379086276265, -0.27283702352499994)
n : (0.4552798120000001, -0.7598638844650001, 0.49960450997500006)
o : (0.3275444810000001, 0.18712959583499994, 0.794370575675)
p : (0.23908312880000016, 1.141122975835, 0.507889826475)
q : (0.8289709796000002, 0.5176241389349999, -0.005219834024999925)
r : (0.9199692627000001, -0.43331888486500003, -0.3008998602249999)
s : (1.3726977160000002, -1.099316960565, 0.291960587775)
t : (1.2466424034, -0.15733139646500005, 0.603044587775)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['l', 'k', 'e'], ['o', 'n', 'g'], ['f', 'm', 'n'], ['o', 't', 'q'], ['p', 'h', 'i'], ['o', 'h', 'p'], ['m', 'r', 's'], ['t', 'q', 'r'], ['d', 'c', 'a'], ['f', 'g', 'n'], ['d', 'c', 'i'], ['d', 'e', 'k'], ['r', 'm', 'l'], ['b', 'a', 'g'], ['d', 'e', 'a'], ['t', 'r', 's'], ['f', 'a', 'g'], ['f', 'e', 'a'], ['h', 'c', 'b'], ['t', 's', 'n'], ['l', 'f', 'e'], ['k', 'q', 'j'], ['p', 'j', 'i'], ['m', 's', 'n'], ['h', 'c', 'i'], ['d', 'j', 'k'], ['c', 'a', 'b'], ['p', 'q', 'j'], ['o', 'q', 'p'], ['o', 't', 'n'], ['f', 'm', 'l'], ['d', 'j', 'i'], ['o', 'h', 'g'], ['k', 'q', 'r'], ['l', 'k', 'r'], ['g', 'h', 'b']]
Coordinate Data:
s : [-4234994707 / 5000000000, 16809435213 / 10000000000, 1175721047 / 5000000000]
d : [11405293481 / 10000000000, 1674151 / 2500000000, 1123131677 / 1000000000]
k : [2423299617 / 10000000000, 2019064329 / 5000000000, 6491920591 / 5000000000]
r : [-3942704881 / 10000000000, 1268681807 / 1250000000, 4140023287 / 5000000000]
n : [352094813 / 5000000000, 3353726113 / 2500000000, 34375359 / 1250000000]
a : [15495520617 / 10000000000, 7971691373 / 10000000000, 6778351431 / 10000000000]
j : [1573698089 / 5000000000, -5535745213 / 10000000000, 10188018721 / 10000000000]
o : [247692867 / 1250000000, 3944969649 / 10000000000, -534531557 / 2000000000]
b : [9515844941 / 5000000000, 2940227401 / 5000000000, -58469707 / 250000000]
m : [-70640269 / 1000000000, 1960712837 / 1000000000, 7999418207 / 10000000000]
l : [1863141277 / 10000000000, 3416837853 / 2500000000, 15622835649 / 10000000000]
q : [-60654441 / 200000000, 320012109 / 5000000000, 665405789 / 1250000000]
f : [7624520771 / 10000000000, 7051033969 / 5000000000, 7460879519 / 10000000000]
p : [1433078229 / 5000000000, -5594964151 / 10000000000, 192149707 / 10000000000]
i : [11373820417 / 10000000000, -3894340781 / 5000000000, 2483922099 / 5000000000]
g : [2480098589 / 2500000000, 9869498369 / 10000000000, -1303498343 / 10000000000]
e : [2679659039 / 2500000000, 4511756629 / 5000000000, 7750226207 / 5000000000]
t : [-56323721 / 78125000, 1847394893 / 2500000000, -379698953 / 5000000000]
h : [5524857943 / 5000000000, -13251117 / 2000000000, -688580591 / 5000000000]
c : [3779138517 / 2000000000, -601969843 / 5000000000, 4717617281 / 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 = 122627111886820556156952316294048350858663078825929965426681 / 249916163842417733072279020996263981041900000000000000000000
Collision distance in [35024027 / 50000000, 14009611 / 20000000] ~ [0.70048, 0.70048]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1159 / 2500, 2319 / 5000] ~ [0.4636, 0.4638]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 194310695017915270259 / 125000000000000000000000000000000000000
rho in [12467901 / 10000000000000000, 112467901 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [1343281 / 734846923, 597529 / 326598632] ~ [0.00183, 0.00183]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-3997 / 20000000, 20143 / 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 [-19985 / 5878775376, 20143 / 5878775376] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [35024027 / 223606798, 14009611 / 89442719] ~ [0.15663, 0.15663]
Success: LHS < CD / |V| ^ .5
Success: existence proven