show/hide visualization coordinates
a : (0.10460557048999991, -0.7454941636749999, -0.19211108059000004)
b : (-0.08589866261000012, -0.7498923824749999, 0.7895657678099999)
c : (-0.72768088991, -1.1787002862749998, 0.15376893080999998)
d : (-0.71241874041, -0.789045447875, -0.7670645418900001)
e : (0.03667111198999995, -0.17219073087499998, -1.00863400239)
f : (0.6245567142899999, 0.10678464812500005, -0.24931276549000003)
g : (0.8399380428899998, -0.5636239539749999, 0.46073427511)
h : (0.4636125646899999, -0.03463949337499994, 1.22136321241)
i : (-0.45190206421, 0.1764244566250001, 0.8788937112099999)
j : (-1.06965649241, -0.6096195082749998, 0.9015655432099999)
k : (-0.82437158851, -0.19150209957499992, 0.026915352409999982)
l : (-0.53665638921, 0.19182844752500008, -0.85072482429)
m : (-0.68910719481, -0.3605148016749999, -1.67028635079)
n : (-0.1659317575100001, 0.4895790578250001, -1.7304485451900002)
o : (0.26153407058999995, 0.793545258425, -0.8790561713900001)
p : (0.6997067746899999, 1.0787788172250001, -0.02664086589000003)
q : (1.1013772677899998, 0.39401758022500005, 0.58143566221)
r : (1.00746378269, 0.7533797634250001, 1.50989584981)
s : (0.26543903298999993, 0.872534392925, 0.85019715741)
t : (-0.14128115351000003, 0.5383504457250001, -5.6314490000042294e-05)
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'], ['q', 's', 'p'], ['c', 'j', 'k'], ['c', 'j', 'b'], ['t', 's', 'p'], ['l', 't', 'o'], ['f', 'e', 'a'], ['l', 'm', 'd'], ['l', 'n', 'o'], ['f', 'e', 'o'], ['h', 'i', 's'], ['l', 't', 'k'], ['e', 'd', 'a'], ['q', 'f', 'g'], ['c', 'b', 'a'], ['q', 'f', 'p'], ['t', 'i', 'k'], ['q', 'r', 's'], ['h', 'r', 's'], ['l', 'd', 'k'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['t', 'i', 's'], ['m', 'e', 'n'], ['f', 'p', 'o'], ['n', 'e', 'o'], ['g', 'f', 'a'], ['l', 'n', 'm'], ['c', 'd', 'k'], ['h', 'g', 'b'], ['h', 'q', 'g'], ['m', 'e', 'd'], ['i', 'j', 'k'], ['i', 'j', 'b']]
Coordinate Data:
k : [13917416663 / 10000000000, 6168103961 / 10000000000, 3958944241 / 10000000000]
t : [7086512313 / 10000000000, -282605373 / 2500000000, 422866091 / 1000000000]
e : [2653494829 / 5000000000, 2987495137 / 5000000000, 14314437789 / 10000000000]
s : [188706903 / 625000000, -1118065241 / 2500000000, -4273873809 / 10000000000]
g : [-2725679651 / 10000000000, 1977864501 / 2000000000, -189622493 / 5000000000]
q : [-53400719 / 100000000, 312907163 / 10000000000, -1586258857 / 10000000000]
h : [1037575131 / 10000000000, 4599477899 / 10000000000, -7985534359 / 10000000000]
c : [12950509677 / 10000000000, 4010021457 / 2500000000, 2690408457 / 10000000000]
l : [1104026467 / 1000000000, 233479849 / 1000000000, 1591918251 / 1250000000]
p : [-1323366969 / 10000000000, -6534705207 / 10000000000, 561813303 / 1250000000]
j : [8185132851 / 5000000000, 323414939 / 312500000, -4787557667 / 10000000000]
i : [509636071 / 500000000, 2488838399 / 10000000000, -4560839347 / 10000000000]
a : [4627645073 / 10000000000, 5854012301 / 5000000000, 6149208571 / 10000000000]
b : [1633171851 / 2500000000, 1175200679 / 1000000000, -3667559913 / 10000000000]
f : [-114373273 / 2000000000, 796309121 / 2500000000, 336061271 / 500000000]
m : [6282386363 / 5000000000, 3929115491 / 5000000000, 20930961273 / 10000000000]
d : [6398944091 / 5000000000, 3035884361 / 2500000000, 743671449 / 625000000]
o : [382295009 / 1250000000, -3682369619 / 10000000000, 13018659479 / 10000000000]
r : [-4400937049 / 10000000000, -3280714669 / 10000000000, -10870860733 / 10000000000]
n : [7333018353 / 10000000000, -642707613 / 10000000000, 21532583217 / 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 = 305523248735818626585302023783415369905953589253933827080969 / 933998896937665147323975242732432936575400000000000000000000
Collision distance in [57193799 / 100000000, 285969 / 500000] ~ [0.57194, 0.57194]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [571 / 2500, 1143 / 5000] ~ [0.2284, 0.2286]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 109335612060446730379376129834817 / 10000000000000000000000000000000000000000
rho in [1307 / 12500000, 10457 / 100000000] ~ [0.0001, 0.0001]
sigma_min ^ 2 / (16 * E ^ .5) in [326041 / 734846923, 145161 / 326598632] ~ [0.00044, 0.00044]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [569787 / 20000000, 361513 / 12500000] ~ [0.02849, 0.02892]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [2848935 / 5878775384, 361513 / 734846922] ~ [0.00048, 0.00049]
CD / |V| ^ .5 in [57193799 / 447213596, 11438760 / 89442719] ~ [0.12789, 0.12789]
Success: LHS < CD / |V| ^ .5
Success: existence proven