show/hide visualization coordinates
a : (0.37261977262999996, 0.734784033565, 0.5566408318900001)
b : (0.02067376083, 0.16568232296500007, 1.29978095849)
c : (0.6877161860300001, -0.20907320823499992, 0.6558766993900002)
d : (1.24266908803, 0.4529737704650001, 0.15216936909000012)
e : (0.5503398724299999, 0.901278531365, -0.41325356870999985)
f : (-0.26209374807, 1.291108275765, 0.02031808929000012)
g : (-0.5822859650700001, 0.8186588798650001, 0.8414566357900001)
h : (-0.69908833657, -0.16258055133499993, 0.6880735052900001)
i : (-0.017618340270000032, -0.800855159235, 1.0461296025900002)
j : (0.5018919363300001, -1.102375561935, 0.2466331864900001)
k : (0.9240351229300001, -0.37972374523499997, -0.30069622220999986)
l : (1.28552251303, 0.37793705046500004, -0.8440901726099999)
m : (0.33443734792999996, 0.09053106466500005, -0.9573809848099999)
n : (-0.34135092367000003, 0.820994330665, -0.8587218293099999)
o : (-0.84318128387, 0.4815578520650001, -0.06314080490999985)
p : (-1.25679512247, -0.4282149820349999, -0.09831157220999986)
q : (-0.49162870397, -1.004181961535, 0.18940771849000015)
r : (0.07676824072999994, -0.811253657035, -0.6104069991099998)
s : (-0.62997044787, -0.13568523943499994, -0.8204730340099999)
t : (-0.87266096907, -1.101562045835, -0.7300114089099998)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'i', 'b'], ['q', 'r', 'j'], ['r', 'j', 'k'], ['c', 'i', 'j'], ['m', 'r', 's'], ['c', 'j', 'k'], ['l', 'm', 'k'], ['n', 'f', 'o'], ['m', 'r', 'k'], ['t', 's', 'p'], ['f', 'e', 'a'], ['q', 'i', 'j'], ['o', 'h', 'g'], ['e', 'd', 'a'], ['h', 'q', 'p'], ['n', 'f', 'e'], ['c', 'b', 'a'], ['h', 'q', 'i'], ['l', 'm', 'e'], ['l', 'd', 'k'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['n', 's', 'o'], ['m', 's', 'n'], ['m', 'e', 'n'], ['q', 't', 'r'], ['p', 's', 'o'], ['h', 'p', 'o'], ['g', 'f', 'a'], ['c', 'd', 'k'], ['t', 'q', 'p'], ['h', 'g', 'b'], ['c', 'i', 'b'], ['l', 'e', 'd'], ['g', 'f', 'o'], ['t', 'r', 's']]
Coordinate Data:
k : [1779025093 / 1250000000, 167169163 / 1250000000, 1037004437 / 5000000000]
t : [-233422511 / 625000000, -2940514851 / 5000000000, -2219142993 / 10000000000]
e : [10495248239 / 10000000000, 1414737607 / 1000000000, 948435409 / 10000000000]
s : [-326963741 / 2500000000, 1888869181 / 5000000000, -780939811 / 2500000000]
g : [-103876267 / 1250000000, 2664235911 / 2000000000, 6747768727 / 5000000000]
q : [3022499 / 400000000, -4907228859 / 10000000000, 6975048281 / 10000000000]
h : [-1999033851 / 10000000000, 3508785243 / 10000000000, 11961706149 / 10000000000]
c : [94952091 / 80000000, 1521929337 / 5000000000, 1163973809 / 1000000000]
l : [3569414929 / 2000000000, 8913961261 / 10000000000, -335993063 / 1000000000]
p : [-757610171 / 1000000000, 106555117 / 1250000000, 2048927687 / 5000000000]
j : [5005384439 / 5000000000, -5889164863 / 10000000000, 7547302961 / 10000000000]
i : [75244783 / 156250000, -718490209 / 2500000000, 7771133561 / 5000000000]
a : [8718047241 / 10000000000, 3120607773 / 2500000000, 2129475883 / 2000000000]
b : [5198587123 / 10000000000, 3395706993 / 5000000000, 18078780681 / 10000000000]
f : [1185456017 / 5000000000, 9022836757 / 5000000000, 5284151989 / 10000000000]
m : [4168111497 / 5000000000, 6039901403 / 10000000000, -140401211 / 312500000]
d : [3483708079 / 2000000000, 9664328461 / 10000000000, 6602664787 / 10000000000]
o : [-859990831 / 2500000000, 9950169277 / 10000000000, 4449563047 / 10000000000]
r : [2879765961 / 5000000000, -1488972907 / 5000000000, -204619779 / 2000000000]
n : [789170139 / 5000000000, 13344534063 / 10000000000, -3506247197 / 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 = 135249026158596592210332622506737999409044974908273784882009 / 210668768103391016414114913564321662320250000000000000000000
Collision distance in [40062403 / 50000000, 80124807 / 100000000] ~ [0.80125, 0.80125]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5587 / 10000, 5589 / 10000] ~ [0.5587, 0.5589]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 2431959039972402795377 / 2000000000000000000000000000000000000000
rho in [110271461 / 100000000000000000, 1110271461 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [31214569 / 11757550768, 3470769 / 1306394528] ~ [0.00265, 0.00266]
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, 20117 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-2221 / 653197264, 20117 / 5878775376] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [40062403 / 223606798, 80124807 / 447213595] ~ [0.17916, 0.17916]
Success: LHS < CD / |V| ^ .5
Success: existence proven