show/hide visualization coordinates
a : (0.3065115112764706, -0.43013501221764694, -0.855847969552941)
b : (1.1073592782764705, -0.29356727161764695, -0.27275954885294096)
c : (0.23809021417647058, -0.579375151617647, 0.13058292344705907)
d : (-0.5909463380235295, -0.460259335517647, -0.41577759605294096)
e : (-0.06601296542352941, 0.390851841782353, -0.42317476745294097)
f : (0.8138414809764706, 0.43064568188235297, -0.8967490524529409)
g : (1.7596537262764707, 0.10653426868235305, -0.9165224791529409)
h : (1.4311283817764706, 0.643100281282353, -0.13924002605294095)
i : (0.6131731638764705, 0.32381263258235304, 0.33930428624705905)
j : (-0.22797222072352946, 0.016669330382353076, 0.784430598547059)
k : (-0.6500691361235295, -0.8457535189176469, 0.505036570447059)
l : (-1.4720876480235294, -0.495881017717647, 0.05573177544705904)
m : (-0.9052235403235294, 0.325670307282353, 0.116711311547059)
n : (-0.17130948352352943, 0.940407443282353, 0.405620312247059)
o : (0.5689876203764707, 1.140400587782353, -0.23622307985294094)
p : (-1.2015209836235294, -0.140370825317647, 0.950386000947059)
q : (-1.5536030612235294, -1.072750242017647, 0.868490740547059)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'n', 'j'], ['b', 'f', 'a'], ['p', 'j', 'm'], ['n', 'e', 'm'], ['i', 'h', 'o'], ['k', 'p', 'j'], ['n', 'o', 'e'], ['p', 'l', 'q'], ['i', 'b', 'h'], ['d', 'l', 'm'], ['d', 'e', 'm'], ['b', 'g', 'f'], ['i', 'j', 'c'], ['d', 'k', 'l'], ['i', 'b', 'c'], ['d', 'c', 'a'], ['h', 'f', 'o'], ['i', 'n', 'o'], ['d', 'e', 'a'], ['d', 'k', 'c'], ['b', 'g', 'h'], ['q', 'k', 'p'], ['f', 'o', 'e'], ['l', 'p', 'm'], ['g', 'f', 'h'], ['f', 'e', 'a'], ['n', 'j', 'm'], ['k', 'l', 'q'], ['c', 'b', 'a'], ['k', 'j', 'c']]
Coordinate Data:
g : [23218231799 / 10000000000, 7023153663 / 10000000000, -1050232409 / 2500000000]
q : [-2478584019 / 2500000000, -1192422861 / 2500000000, 13649202561 / 10000000000]
e : [2480782441 / 5000000000, 4933164697 / 5000000000, 732547481 / 10000000000]
i : [470137047 / 400000000, 4597968651 / 5000000000, 4178669009 / 5000000000]
m : [-3430540867 / 10000000000, 9214514049 / 10000000000, 6131408271 / 10000000000]
j : [3341972329 / 10000000000, 153112607 / 250000000, 12808601141 / 10000000000]
h : [9966489177 / 5000000000, 12388813789 / 10000000000, 714378979 / 2000000000]
o : [565578537 / 500000000, 8680908427 / 5000000000, 2602064357 / 10000000000]
p : [-63935153 / 100000000, 4554102723 / 10000000000, 2893631033 / 2000000000]
k : [-35159873 / 400000000, -2499724213 / 10000000000, 500733043 / 500000000]
c : [4001298339 / 5000000000, 8202973 / 500000000, 627012439 / 1000000000]
n : [3908599701 / 10000000000, 15361885409 / 10000000000, 4510249139 / 5000000000]
d : [-71942211 / 2500000000, 1355217621 / 10000000000, 161303839 / 2000000000]
b : [16695287319 / 10000000000, 151106913 / 500000000, 2236699667 / 10000000000]
a : [8686809649 / 10000000000, 828230427 / 5000000000, -179709227 / 500000000]
l : [-1137397743 / 1250000000, 999000799 / 10000000000, 552161291 / 1000000000]
f : [6880054673 / 5000000000, 2052853559 / 2000000000, -4003195369 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 55555555529753882781603379193311870586743497434708409524569 / 111111111095295812555227253145368990253800000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [304 / 625, 2433 / 5000] ~ [0.4864, 0.4866]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 14425701468018253671 / 20000000000000000000000000000000000000
rho in [212321259 / 250000000000000000, 2712321259 / 250000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [739328 / 335410197, 5919489 / 2683281572] ~ [0.0022, 0.00221]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19991 / 100000000, 503 / 2500000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-19991 / 5366563144, 2515 / 670820393] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710678 / 412310563, 70710679 / 412310562] ~ [0.1715, 0.1715]
Success: LHS < CD / |V| ^ .5
Success: existence proven