show/hide visualization coordinates
a : (-1.0579589987777778, 1.4641876020777778, -0.026424873644444458)
b : (-0.44413250977777785, 0.9760420337777778, 0.5940765999555555)
c : (-0.4884646370777779, 1.9748430069777778, 0.6176000316555555)
d : (-1.3840660024777778, 2.330951995977778, 0.3508685770555555)
e : (-0.6322221005777777, 2.323964925577778, -0.30841608164444445)
f : (-0.06830590577777784, 1.5111631568777777, -0.16244089294444441)
g : (-0.5586756692777778, 0.6595789836777778, -0.34756397484444446)
h : (-0.37086993477777785, 0.0015548609777777944, 0.3816216017555556)
i : (0.3438755921222222, 0.6335256295777778, 0.08239149015555558)
j : (0.05351097362222218, -0.11261423232222223, -0.5167274542444444)
k : (-0.17154737747777782, -0.9152233919222221, 0.03562253125555559)
l : (0.5762937069222221, -0.3117067455222222, 0.3121157528555556)
m : (0.6763114976222222, -0.8945636266222221, -0.49433988904444437)
n : (0.20473852992222216, -1.7625721241222223, -0.33887674824444447)
o : (0.6672580960222222, -1.3019609307222222, 0.4187744380555556)
p : (1.203622763122222, -1.7244174781222221, -0.3119119639444444)
q : (0.7432430738222222, -2.554693477222222, -0.6261167249444444)
r : (0.7073889028222222, -2.2980601889222223, 0.33974758075555556)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['g', 'i', 'j'], ['h', 'l', 'k'], ['h', 'i', 'l'], ['o', 'p', 'r'], ['o', 'l', 'k'], ['o', 'p', 'm'], ['p', 'n', 'q'], ['p', 'r', 'q'], ['a', 'b', 'c'], ['n', 'k', 'm'], ['j', 'l', 'm'], ['b', 'i', 'h'], ['j', 'k', 'm'], ['g', 'h', 'j'], ['l', 'i', 'j'], ['b', 'c', 'f'], ['d', 'a', 'c'], ['a', 'f', 'e'], ['g', 'i', 'f'], ['a', 'b', 'g'], ['e', 'c', 'f'], ['p', 'n', 'm'], ['b', 'h', 'g'], ['n', 'r', 'q'], ['o', 'l', 'm'], ['d', 'a', 'e'], ['o', 'n', 'r'], ['o', 'n', 'k'], ['a', 'g', 'f'], ['b', 'i', 'f'], ['d', 'e', 'c'], ['h', 'k', 'j']]
Coordinate Data:
b : [8461808477 / 10000000000, -4176036711 / 10000000000, -400349291 / 10000000000]
m : [-2742631597 / 10000000000, 14530019893 / 10000000000, 10483815599 / 10000000000]
p : [-2003936063 / 2500000000, 2853569801 / 1250000000, 2164884087 / 2500000000]
o : [-2652097581 / 10000000000, 9301996467 / 5000000000, 169084041 / 1250000000]
f : [4703542437 / 10000000000, -4763623971 / 5000000000, 3582412819 / 5000000000]
d : [4465285851 / 2500000000, -17725136333 / 10000000000, 1015865469 / 5000000000]
e : [2068540877 / 2000000000, -17655265629 / 10000000000, 344983101 / 400000000]
c : [35620519 / 40000000, -14164046443 / 10000000000, -79447951 / 1250000000]
r : [-3053405649 / 10000000000, 7141246379 / 2500000000, 2142940901 / 10000000000]
i : [290863729 / 5000000000, -750872669 / 10000000000, 4716501807 / 10000000000]
n : [12331863 / 62500000, 5802526217 / 2500000000, 8929184191 / 10000000000]
h : [7729182727 / 10000000000, 5568835017 / 10000000000, 1724200691 / 10000000000]
l : [-174245369 / 1000000000, 4350725541 / 5000000000, 120962959 / 500000000]
g : [1200905009 / 1250000000, -101140621 / 1000000000, 9016056457 / 10000000000]
j : [3485373643 / 10000000000, 134210519 / 200000000, 10707691251 / 10000000000]
a : [14600073367 / 10000000000, -4528746197 / 5000000000, 1160933089 / 2000000000]
q : [-3411947359 / 10000000000, 31131318399 / 10000000000, 5900791979 / 5000000000]
k : [2867978577 / 5000000000, 7368308773 / 5000000000, 1296047849 / 2500000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 124982489872197289012516967694949260261752537257378264682481 / 250075995675276967051616426571820134710600000000000000000000
Collision distance in [70694981 / 100000000, 35347491 / 50000000] ~ [0.70695, 0.70695]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [403 / 1250, 1613 / 5000] ~ [0.3224, 0.3226]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 3305730292506816328672910370172847 / 5000000000000000000000000000000000000000
rho in [8131 / 10000000, 81311 / 100000000] ~ [0.00081, 0.00081]
sigma_min ^ 2 / (16 * E ^ .5) in [162409 / 173205081, 2601769 / 2771281292] ~ [0.00094, 0.00094]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [4086847 / 20000000, 20509469 / 100000000] ~ [0.20434, 0.20509]
LHS DEN := 8 * |E| ^ .5 in [692820323 / 12500000, 173205081 / 3125000] ~ [55.42563, 55.42563]
LHS := (LHS NUM) / (LHS DEN) in [20434235 / 5542562592, 20509469 / 5542562584] ~ [0.00369, 0.0037]
CD / |V| ^ .5 in [70694981 / 424264069, 3927499 / 23570226] ~ [0.16663, 0.16663]
Success: LHS < CD / |V| ^ .5
Success: existence proven