show/hide visualization coordinates
a : (0.53098739425, 0.652767407165, -0.32544480155999966)
b : (0.030475471749999983, 0.6970413096650001, 0.5391520045400002)
c : (0.99131815205, 0.971768359965, 0.5030079644400003)
d : (1.4346142938500002, 0.29695302436500004, -0.08700287735999968)
e : (1.10011678935, 0.223103286365, -1.0265014859599997)
f : (0.10470387945000004, 0.13728370586500005, -1.0687878708599996)
g : (-0.45163057585, 0.46809554346500004, -0.3065179044599997)
h : (-0.83598484685, 0.19920489786500006, 0.5766409799400003)
i : (-0.06770861065, -0.09061735113499997, 1.1473902144400003)
j : (0.60326474945, 0.621109919165, 1.3553302125400004)
k : (0.75206747595, 0.004077331465, 0.5825892894400002)
l : (0.77032447575, -0.410930135335, -0.32704551885999966)
m : (0.68412939815, -0.6456379355349999, -1.2952823994599996)
n : (-0.09637291395000003, -0.762314636535, -0.6811141095599997)
o : (-0.84357930285, -0.165513901335, -0.9735375944599998)
p : (-1.4137020045500002, 0.20363681216500007, -0.23958401585999972)
q : (-1.63898365365, -0.39488413223499996, 0.5291947935400003)
r : (-0.77642987415, -0.7480630069349999, 0.8915008243400002)
s : (0.020027503549999992, -0.616407000835, 0.30131242944000025)
t : (-0.89763780105, -0.6406734976349999, -0.09530013425999972)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'i', 'b'], ['h', 'q', 'r'], ['t', 'p', 'o'], ['h', 'p', 'g'], ['c', 'j', 'k'], ['c', 'j', 'b'], ['n', 'f', 'o'], ['m', 'f', 'n'], ['f', 'e', 'a'], ['i', 's', 'k'], ['n', 't', 'o'], ['n', 't', 's'], ['e', 'd', 'a'], ['h', 'q', 'p'], ['c', 'b', 'a'], ['l', 'm', 'e'], ['l', 'd', 'k'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['o', 'p', 'g'], ['q', 't', 'r'], ['r', 'i', 's'], ['h', 'r', 'i'], ['g', 'f', 'a'], ['l', 'n', 'm'], ['c', 'd', 'k'], ['m', 'f', 'e'], ['t', 'q', 'p'], ['h', 'g', 'b'], ['l', 'e', 'd'], ['g', 'f', 'o'], ['i', 'j', 'k'], ['i', 'j', 'b'], ['t', 'r', 's'], ['l', 'n', 's'], ['l', 's', 'k']]
Coordinate Data:
k : [1167690243 / 1000000000, 5574648213 / 10000000000, 11075079487 / 10000000000]
t : [-241007517 / 500000000, -436430039 / 5000000000, 17184741 / 40000000]
e : [3789348891 / 2500000000, 3882453881 / 5000000000, -5015828267 / 10000000000]
s : [2178251353 / 5000000000, -63019511 / 1000000000, 8262310887 / 10000000000]
g : [-45009761 / 1250000000, 10214830333 / 10000000000, 546001887 / 2500000000]
q : [-6116804433 / 5000000000, 198129197 / 1250000000, 164705227 / 156250000]
h : [-2101810399 / 5000000000, 7525923877 / 10000000000, 1376949549 / 1250000000]
c : [14069409191 / 10000000000, 7625779249 / 5000000000, 10279266237 / 10000000000]
l : [2964868107 / 2500000000, 284914709 / 2000000000, 494682851 / 2500000000]
p : [-79846339 / 80000000, 378512151 / 500000000, 1426673217 / 5000000000]
j : [2037775033 / 2000000000, 1174497409 / 1000000000, 9401244359 / 5000000000]
i : [869785391 / 2500000000, 4627701387 / 10000000000, 16723088737 / 10000000000]
a : [9466101613 / 10000000000, 1206154897 / 1000000000, 1994738577 / 10000000000]
b : [1115245597 / 2500000000, 2500857599 / 2000000000, 5320353319 / 5000000000]
f : [1040653293 / 2000000000, 6906711957 / 10000000000, -1359673029 / 2500000000]
m : [2749380413 / 2500000000, -922504457 / 10000000000, -3851818701 / 5000000000]
d : [18502370609 / 10000000000, 4251702571 / 5000000000, 4379157819 / 10000000000]
o : [-2139782679 / 5000000000, 775747177 / 2000000000, -560773669 / 1250000000]
r : [-3608071071 / 10000000000, -1946755171 / 10000000000, 3541048709 / 2500000000]
n : [3192498531 / 10000000000, -2089271467 / 10000000000, -1561954503 / 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 = 556325877729410004011417811434531215155205370992807262809 / 1111108962973698351927559166722943182840000000000000000000
Collision distance in [8844969 / 12500000, 70759753 / 100000000] ~ [0.7076, 0.7076]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [117 / 250, 2341 / 5000] ~ [0.468, 0.4682]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 13495493952437018274543 / 10000000000000000000000000000000000000000
rho in [116170107 / 100000000000000000, 1116170107 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [1368900 / 734846923, 5480281 / 2939387688] ~ [0.00186, 0.00186]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9993 / 50000000, 20141 / 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 [-3331 / 979795896, 20141 / 5878775376] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [17689938 / 111803399, 70759753 / 447213595] ~ [0.15822, 0.15822]
Success: LHS < CD / |V| ^ .5
Success: existence proven