show/hide visualization coordinates
a : (-0.7956733300157894, 0.14606084559473687, 0.40315957327894747)
b : (-0.08647880041578948, -0.3245229404052631, 0.9281029711789475)
c : (-0.5123256525157894, 0.5033714787947369, 1.2931287208789475)
d : (-0.7611723131157895, 1.1334676869947369, 0.5575668901789474)
e : (-1.3348336091157895, 0.761232662494737, -0.17205589262105253)
f : (-0.8876785972157895, -0.037010087405263126, -0.5756099355210526)
g : (-0.26289886701578946, -0.5863881656052631, -0.02075590732105259)
h : (0.5235501675842105, -0.9676282834052631, 0.46523339347894743)
i : (0.7974093490842105, -0.012676552505263117, 0.5795396928789474)
j : (0.4581428090842105, 0.3263596219947369, 1.4570082641789475)
k : (0.1662223733842106, 0.762508433794737, 0.6057989127789474)
l : (-0.33876566211578946, 0.7357291417947369, -0.25691252302105255)
m : (0.04557144608421054, 0.08626201259473687, -0.9130214838210525)
n : (-0.3989331204157895, -0.8064792208052631, -0.9867203957210525)
o : (0.3119075958842105, -1.2752785826052633, -0.46241227382105254)
p : (0.8479142583842105, -0.4428580921052631, -0.32178851782105256)
q : (0.6402291865842105, 0.5322466814947369, -0.24408224652105254)
r : (1.0258645064842105, 0.16921128819473685, -1.0923106935210525)
s : (0.5619482593842104, -0.7036079289052631, -1.2438685491210526)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'q', 'p'], ['r', 'q', 'p'], ['h', 'p', 'o'], ['d', 'a', 'c'], ['d', 'a', 'e'], ['k', 'i', 'q'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['l', 'e', 'f'], ['m', 'n', 'f'], ['s', 'n', 'o'], ['s', 'r', 'p'], ['d', 'k', 'c'], ['b', 'j', 'i'], ['b', 'g', 'a'], ['s', 'r', 'm'], ['s', 'p', 'o'], ['l', 'm', 'q'], ['s', 'm', 'n'], ['l', 'm', 'f'], ['b', 'a', 'c'], ['g', 'n', 'o'], ['j', 'k', 'i'], ['b', 'j', 'c'], ['g', 'n', 'f'], ['g', 'h', 'o'], ['b', 'g', 'h'], ['i', 'h', 'p'], ['l', 'k', 'q'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['r', 'm', 'q'], ['g', 'a', 'f']]
Coordinate Data:
d : [-3751593213 / 10000000000, 766007577 / 500000000, 1367713193 / 1250000000]
c : [-1263126607 / 10000000000, 4509594729 / 5000000000, 18297323851 / 10000000000]
n : [-64600643 / 5000000000, -2039658769 / 5000000000, -900233463 / 2000000000]
s : [296237891 / 312500000, -3050604619 / 10000000000, -7072648849 / 10000000000]
q : [1282802723 / 1250000000, 1861588297 / 2000000000, 2925214177 / 10000000000]
p : [6169636251 / 5000000000, -443106251 / 10000000000, 268518933 / 1250000000]
i : [11834223409 / 10000000000, 771741829 / 2000000000, 11161433571 / 10000000000]
m : [4315844379 / 10000000000, 1212023699 / 2500000000, -941044549 / 2500000000]
a : [-2048301691 / 5000000000, 2723041563 / 5000000000, 75181059 / 80000000]
b : [1497670957 / 5000000000, 370122633 / 5000000000, 7323533177 / 5000000000]
r : [14118774983 / 10000000000, 177424611 / 312500000, -5557070293 / 10000000000]
e : [-9488206173 / 10000000000, 2319560259 / 2000000000, 911369429 / 2500000000]
j : [8441558009 / 10000000000, 724907089 / 1000000000, 4984029821 / 2500000000]
k : [1380588413 / 2500000000, 362829969 / 312500000, 1142402577 / 1000000000]
l : [472473297 / 10000000000, 1417845761 / 1250000000, 699227853 / 2500000000]
h : [4547815797 / 5000000000, -1422702041 / 2500000000, 10018370577 / 10000000000]
f : [-2508328027 / 5000000000, 903843449 / 2500000000, -390062713 / 10000000000]
g : [9618291 / 78125000, -939203493 / 5000000000, 5158477569 / 10000000000]
o : [6979205877 / 10000000000, -2191827789 / 2500000000, 46369619 / 625000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 10375400017262060674941323341392244207584643778009820228603 / 20833065138186723041877876156187452464262500000000000000000
Collision distance in [70570929 / 100000000, 7057093 / 10000000] ~ [0.70571, 0.70571]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2151 / 10000, 2153 / 10000] ~ [0.2151, 0.2153]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 61518654081848641920363539056623 / 5000000000000000000000000000000000000000
rho in [2773 / 25000000, 11093 / 100000000] ~ [0.00011, 0.00011]
sigma_min ^ 2 / (16 * E ^ .5) in [4626801 / 11426285488, 4635409 / 11426285472] ~ [0.0004, 0.00041]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [3157873 / 100000000, 3201653 / 100000000] ~ [0.03158, 0.03202]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [3157873 / 5713142744, 457379 / 816163248] ~ [0.00055, 0.00056]
CD / |V| ^ .5 in [70570929 / 435889895, 35285465 / 217944947] ~ [0.1619, 0.1619]
Success: LHS < CD / |V| ^ .5
Success: existence proven