show/hide visualization coordinates
a : (-0.609881680295, 0.29306636219500004, 0.588327427995)
b : (-0.47091915809499996, 1.263467484995, 0.390815204795)
c : (-1.364758956395, 0.843981066495, 0.23244361739499997)
d : (-1.1030668453949999, -0.003437679004999916, -0.22950736360500001)
e : (-0.39181770689499995, -0.5858428758049999, 0.16410265889499998)
f : (0.157182773805, -0.25021902240499994, 0.929579700495)
g : (0.23569164110500007, 0.745054741595, 0.8724264649950001)
h : (0.23968390270500006, 0.786784164595, -0.12669450720500003)
i : (-0.684674620095, 0.8634812273950001, -0.500430887005)
j : (-0.9884473953949999, 0.215155633595, -1.1985684273050001)
k : (-0.570727248495, -0.6105447736049999, -0.8194527245050001)
l : (0.0021283368050000195, -1.313335636205, -0.397645326005)
m : (0.36241284780500005, -1.138492564505, 0.518665195195)
n : (1.052144686805, -0.41443818740499994, 0.5147601732949999)
o : (0.9681633011049999, 0.20900186589500003, 1.2921079891949998)
p : (1.082237894405, 0.5743113340950001, 0.368237879495)
q : (0.7658878442050001, -0.030101173204999943, -0.362931161605)
r : (-0.031202772094999998, 0.22659447749500006, -0.9095149999050001)
s : (0.40201655410500003, -0.664455407205, -1.044981299005)
t : (0.9479466003050001, -1.0100310390049998, -0.281739615605)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'i', 'b'], ['r', 'i', 'j'], ['h', 'q', 'r'], ['n', 't', 'q'], ['r', 'j', 'k'], ['e', 'd', 'k'], ['h', 'p', 'g'], ['q', 't', 's'], ['n', 'f', 'o'], ['l', 't', 'm'], ['m', 'f', 'n'], ['f', 'e', 'a'], ['e', 'd', 'a'], ['h', 'q', 'p'], ['c', 'b', 'a'], ['q', 'r', 's'], ['l', 't', 's'], ['l', 'm', 'e'], ['m', 't', 'n'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['o', 'p', 'g'], ['n', 'q', 'p'], ['h', 'r', 'i'], ['r', 's', 'k'], ['j', 'd', 'k'], ['c', 'i', 'd'], ['g', 'f', 'a'], ['l', 'e', 'k'], ['j', 'i', 'd'], ['m', 'f', 'e'], ['h', 'g', 'b'], ['c', 'i', 'b'], ['g', 'f', 'o'], ['o', 'n', 'p'], ['l', 's', 'k']]
Coordinate Data:
k : [3518231 / 5000000000, -513066061 / 5000000000, -88862209 / 312500000]
t : [303875499 / 200000000, -627624347 / 1250000000, 2533540401 / 10000000000]
e : [898065939 / 5000000000, -97389143 / 1250000000, 3495981573 / 5000000000]
s : [1216809311 / 1250000000, -782619229 / 5000000000, -5098876433 / 10000000000]
g : [4035612679 / 5000000000, 1252986303 / 1000000000, 14075201207 / 10000000000]
q : [13373187389 / 10000000000, 2389151941 / 5000000000, 1721624941 / 10000000000]
h : [4055573987 / 5000000000, 647357863 / 500000000, 816798297 / 2000000000]
c : [-7933280617 / 10000000000, 13519126279 / 10000000000, 7675372731 / 10000000000]
l : [1147118463 / 2000000000, -2013510187 / 2500000000, 1374483297 / 10000000000]
p : [16536687891 / 10000000000, 2164485791 / 2000000000, 1129164419 / 1250000000]
j : [-4170165007 / 10000000000, 144617439 / 200000000, -1658686929 / 2500000000]
i : [-566218627 / 5000000000, 857132993 / 625000000, 346627687 / 10000000000]
a : [-24031741 / 625000000, 2002494809 / 2500000000, 11234210837 / 10000000000]
b : [502558683 / 5000000000, 276781101 / 156250000, 1851817721 / 2000000000]
f : [1457227337 / 2000000000, 257712539 / 1000000000, 7323366781 / 5000000000]
m : [373537497 / 400000000, -6305610031 / 10000000000, 10537588509 / 10000000000]
d : [-5316359507 / 10000000000, 630617353 / 1250000000, 3055862921 / 10000000000]
o : [7697970979 / 5000000000, 7169334273 / 10000000000, 18272016449 / 10000000000]
r : [2701140613 / 5000000000, 7345260389 / 10000000000, -1872106721 / 5000000000]
n : [3247151163 / 2000000000, 46746687 / 500000000, 1049853829 / 1000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 244082097846720400453029121097987089553791145173657993969 / 409362554016700669232663625893108727537500000000000000000
Collision distance in [38608587 / 50000000, 3088687 / 4000000] ~ [0.77217, 0.77217]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1083 / 2500, 2167 / 5000] ~ [0.4332, 0.4334]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 2447963973579946209229 / 1250000000000000000000000000000000000000
rho in [27988363 / 20000000000000000, 227988363 / 20000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [1172889 / 734846923, 4695889 / 2939387688] ~ [0.0016, 0.0016]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9991 / 50000000, 4031 / 20000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-9991 / 2939387688, 20155 / 5878775376] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [38608587 / 223606798, 15443435 / 89442719] ~ [0.17266, 0.17266]
Success: LHS < CD / |V| ^ .5
Success: existence proven