show/hide visualization coordinates
a : (0.7158695509263158, 0.088951617731579, 0.7290220111684211)
b : (1.0132185495263157, 0.547929878131579, -0.10818915063157897)
c : (0.6207297584263158, 1.0805729289315789, 0.641640115568421)
d : (-0.1922500027736842, 0.507386853231579, 0.7442151098684211)
e : (-0.0876903353736842, -0.46771805166842106, 0.9397597341684211)
f : (0.8031164065263158, -0.9037723914684209, 0.8120101343684211)
g : (1.0626762574263158, -0.448492858568421, -0.03966423383157891)
h : (1.2981266685263158, 0.005906469331579012, -0.8987825918315789)
i : (0.5811706883263158, 0.695955702531579, -0.997808731831579)
j : (0.06315849702631582, 0.856067798931579, -0.1575543136315789)
k : (-0.8017309253736842, 0.368944631031579, -0.036404361531578944)
l : (-1.0009675166736842, -0.07326996586842105, 0.8380960867684211)
m : (-0.7798514304736841, -0.9427522675684211, 0.39638554306842105)
n : (0.15507952422631582, -0.8582603133684209, 0.05176224686842107)
o : (0.34642360792631577, -0.23014744186842107, -0.7024669360315788)
p : (-0.37751524857368424, 0.417285768431579, -0.9406743408315789)
q : (-1.3296078709736843, 0.12522612093157898, -0.850005752131579)
r : (-1.4911545564736841, -0.35373818236842103, 0.01283598126842106)
s : (-0.5988016221736843, -0.41607629646842104, -0.4341765508315789)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['d', 'a', 'c'], ['d', 'a', 'e'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['j', 'i', 'p'], ['l', 'k', 'r'], ['s', 'n', 'o'], ['d', 'k', 'j'], ['k', 'q', 'p'], ['b', 'j', 'i'], ['b', 'g', 'a'], ['m', 'e', 'n'], ['d', 'j', 'c'], ['s', 'r', 'm'], ['s', 'p', 'o'], ['s', 'm', 'n'], ['k', 'r', 'q'], ['b', 'a', 'c'], ['g', 'n', 'o'], ['i', 'p', 'o'], ['e', 'n', 'f'], ['k', 'j', 'p'], ['b', 'j', 'c'], ['g', 'n', 'f'], ['g', 'h', 'o'], ['b', 'g', 'h'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['l', 'm', 'e'], ['l', 'r', 'm'], ['s', 'r', 'q'], ['i', 'h', 'o'], ['g', 'a', 'f'], ['s', 'q', 'p']]
Coordinate Data:
d : [6970704177 / 10000000000, 749882467 / 10000000000, -1581488521 / 5000000000]
c : [-231818687 / 2000000000, -498197829 / 1000000000, -2137227099 / 10000000000]
n : [3497408907 / 10000000000, 14406354133 / 10000000000, 940387897 / 2500000000]
s : [11036220371 / 10000000000, 2496128491 / 2500000000, 1724187913 / 2000000000]
q : [18344282859 / 10000000000, 457148979 / 1000000000, 6389615789 / 5000000000]
p : [1764671327 / 2000000000, 330178663 / 2000000000, 2737183493 / 2000000000]
i : [-381751367 / 5000000000, -567903013 / 5000000000, 114058091 / 80000000]
m : [6423359227 / 5000000000, 610050947 / 400000000, 157659313 / 5000000000]
a : [-13190571 / 62500000, 2467117411 / 5000000000, -602209211 / 2000000000]
b : [-2541990673 / 5000000000, 172226109 / 5000000000, 5361065563 / 10000000000]
e : [5925107503 / 10000000000, 2625232879 / 2500000000, -1023684657 / 2000000000]
r : [9979874857 / 5000000000, 9361132823 / 10000000000, 1037703561 / 2500000000]
j : [4416619179 / 10000000000, -273692699 / 1000000000, 5854717193 / 10000000000]
k : [13065513403 / 10000000000, 2134304689 / 10000000000, 580402209 / 1250000000]
l : [3764469829 / 2500000000, 3278225329 / 5000000000, -4101786811 / 10000000000]
h : [-991632817 / 1250000000, 2882343153 / 5000000000, 530679999 / 400000000]
f : [-745739979 / 2500000000, 7430737457 / 5000000000, -3840927287 / 10000000000]
g : [-223142337 / 400000000, 2061735917 / 2000000000, 935163279 / 2000000000]
o : [158396807 / 1000000000, 4062612709 / 5000000000, 11303843417 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 6959687354048552319452585092903607837356409118923226314161 / 15492262137440726940788191673018137319000000000000000000000
Collision distance in [8378137 / 12500000, 67025097 / 100000000] ~ [0.67025, 0.67025]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [4021 / 10000, 4023 / 10000] ~ [0.4021, 0.4023]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1015470418866773343089143 / 2500000000000000000000000000000000000000
rho in [12596319 / 625000000000000, 18846319 / 625000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [16168441 / 11426285488, 5394843 / 3808761824] ~ [0.00142, 0.00142]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9857 / 50000000, 20429 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-9857 / 2856571368, 20429 / 5713142736] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [67025096 / 435889895, 67025097 / 435889894] ~ [0.15377, 0.15377]
Success: LHS < CD / |V| ^ .5
Success: existence proven