show/hide visualization coordinates
a : (0.6743265348611112, 0.43223823447222215, -0.9200813151666665)
b : (-0.17201852143888885, 0.7322518893722222, -0.4799769499666667)
c : (0.6185956202611111, 0.47851723917222216, 0.07729139303333338)
d : (0.7857189526611112, -0.39806365092777785, -0.3740130882666666)
e : (-0.10833435343888886, -0.16900046462777785, -0.7589789858666667)
f : (-0.1594269293388888, 0.5409063529722221, -1.4614189184666666)
g : (-0.9683878063388889, 0.31564856747222214, -0.9184260736666665)
h : (-0.9978542930388887, 0.5493289676722222, 0.053440787933333345)
i : (-0.17905193433888889, 0.9035286738722221, 0.5052208951333333)
j : (0.4043170045611112, 0.2881791906722222, 1.0353394617333334)
k : (1.1025395002611111, -0.24956483802777785, 0.5627754913333334)
l : (0.8595173923611112, -1.1701847566277777, 0.25716263093333336)
m : (-0.04092281603888881, -0.8243523752277778, -0.006669503066666638)
n : (-0.9221159499388889, -0.4070242719277778, -0.2287863978666666)
o : (-1.7768988519388889, 0.09109381997222216, -0.37447290046666665)
p : (-0.39268428343888884, -0.07232391442777786, 0.5507505038333333)
q : (0.2881068964611112, -0.6993733359277777, 0.9293431506333334)
r : (0.9845738378611112, -0.34180532792777785, 1.5514998182333335)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['c', 'i', 'b'], ['l', 'k', 'd'], ['e', 'n', 'g'], ['e', 'a', 'f'], ['e', 'm', 'd'], ['q', 'p', 'm'], ['q', 'k', 'r'], ['h', 'g', 'o'], ['c', 'a', 'd'], ['n', 'p', 'm'], ['q', 'k', 'l'], ['q', 'p', 'j'], ['h', 'i', 'b'], ['h', 'n', 'o'], ['h', 'n', 'p'], ['e', 'a', 'd'], ['a', 'f', 'b'], ['q', 'r', 'j'], ['f', 'g', 'b'], ['c', 'j', 'i'], ['h', 'g', 'b'], ['l', 'q', 'm'], ['e', 'f', 'g'], ['h', 'p', 'i'], ['r', 'k', 'j'], ['n', 'g', 'o'], ['e', 'n', 'm'], ['l', 'm', 'd'], ['c', 'k', 'j'], ['c', 'a', 'b'], ['p', 'j', 'i'], ['c', 'k', 'd']]
Coordinate Data:
l : [-175076949 / 500000000, 3368739077 / 2000000000, 382040567 / 2500000000]
k : [-5931760059 / 10000000000, 7637496199 / 10000000000, -11937237 / 78125000]
c : [-1092321259 / 10000000000, 356675427 / 10000000000, 3326874647 / 10000000000]
i : [6884154287 / 10000000000, -97335973 / 250000000, -476210187 / 5000000000]
n : [14314794443 / 10000000000, 4606045269 / 5000000000, 1596913139 / 2500000000]
a : [-329926081 / 2000000000, 409732737 / 5000000000, 13300601729 / 10000000000]
f : [6687904237 / 10000000000, -267215711 / 10000000000, 9356988881 / 5000000000]
r : [-950420687 / 2000000000, 4279950549 / 5000000000, -2283041921 / 2000000000]
b : [3406910079 / 5000000000, -87226843 / 400000000, 8899558077 / 10000000000]
d : [-2763554583 / 10000000000, 1140310541 / 1250000000, 391995973 / 500000000]
e : [3088489239 / 5000000000, 1366370493 / 2000000000, 2922394609 / 2500000000]
q : [2212565979 / 10000000000, 6067790589 / 5000000000, -5193642929 / 10000000000]
o : [22862623463 / 10000000000, 4230909619 / 10000000000, 3922258791 / 5000000000]
m : [21495559 / 39062500, 13385371571 / 10000000000, 520810451 / 1250000000]
j : [525232449 / 5000000000, 282506989 / 1250000000, -156340151 / 250000000]
g : [14777513007 / 10000000000, 62042567 / 312500000, 6642024657 / 5000000000]
p : [4510238889 / 5000000000, 5865086963 / 10000000000, -1407716461 / 10000000000]
h : [7536088937 / 5000000000, -175720929 / 5000000000, 1782690349 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 470737539249706540485228121157073627535591797833025081144889 / 997199135599381614673444334719720259430200000000000000000000
Collision distance in [68706601 / 100000000, 34353301 / 50000000] ~ [0.68707, 0.68707]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2421 / 5000, 1211 / 2500] ~ [0.4842, 0.4844]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1964713218014135307543 / 2000000000000000000000000000000000000000
rho in [495569523 / 500000000000000000, 5495569523 / 500000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [217083 / 102640048, 1466521 / 692820323] ~ [0.00211, 0.00212]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19989 / 100000000, 10063 / 50000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [692820323 / 12500000, 173205081 / 3125000] ~ [55.42563, 55.42563]
LHS := (LHS NUM) / (LHS DEN) in [-19989 / 5542562584, 10063 / 2771281292] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [68706601 / 424264069, 34353301 / 212132034] ~ [0.16194, 0.16194]
Success: LHS < CD / |V| ^ .5
Success: existence proven