show/hide visualization coordinates
a : (-0.7663241849352942, 1.2164344563764704, -0.2397412108529411)
b : (-0.9345388570352942, 0.5311791223764705, 0.46886935654705886)
c : (-0.20823772113529412, 1.2077992788764704, 0.5899966594470588)
d : (0.1105369878647059, 1.6968478327764704, -0.22192340645294112)
e : (-0.07346839783529413, 1.0183032631764704, -0.9330628321529411)
f : (-0.43001980373529414, 0.28211379027647043, -0.3578270806529411)
g : (-0.6627324409352942, -0.41898492742352955, 0.3161947492470589)
h : (-0.006952872235294116, 0.23393327297647049, 0.6952079184470589)
i : (0.36905547296470587, 0.7413000511764706, -0.08016081595294111)
j : (0.41063760936470584, 0.14480282477647044, -0.8816980776529411)
k : (-0.026788463735294143, -0.6304409619235295, -0.4260057571529411)
l : (-0.35326607923529413, -1.3594481270235295, 0.17562612764705887)
m : (0.16125910596470583, -0.7484020322235295, 0.7771961611470589)
n : (0.5777614705647058, -0.2304504374235295, 0.030033573947058856)
o : (0.9045941535647058, -0.7186219446235296, -0.7792061826529411)
p : (0.6281884925647058, -1.2291657990235296, 0.03500808404705891)
q : (0.3002955279647058, -1.7371996631235294, 0.8314927330470588)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'n', 'j'], ['i', 'e', 'j'], ['b', 'f', 'a'], ['g', 'l', 'm'], ['n', 'p', 'm'], ['n', 'o', 'j'], ['i', 'h', 'c'], ['k', 'o', 'p'], ['g', 'k', 'f'], ['d', 'i', 'c'], ['q', 'l', 'p'], ['i', 'n', 'h'], ['b', 'g', 'f'], ['f', 'e', 'j'], ['g', 'h', 'm'], ['n', 'h', 'm'], ['k', 'f', 'j'], ['d', 'c', 'a'], ['d', 'i', 'e'], ['l', 'q', 'm'], ['k', 'o', 'j'], ['d', 'e', 'a'], ['b', 'g', 'h'], ['n', 'o', 'p'], ['b', 'h', 'c'], ['k', 'l', 'p'], ['p', 'q', 'm'], ['f', 'e', 'a'], ['g', 'l', 'k'], ['c', 'b', 'a']]
Coordinate Data:
a : [-756799541 / 2000000000, 17372943721 / 10000000000, 2849805997 / 10000000000]
g : [-549616053 / 2000000000, 1018749883 / 10000000000, 4204582799 / 5000000000]
q : [53767183 / 78125000, -6081698737 / 5000000000, 3390536359 / 2500000000]
i : [3784899437 / 5000000000, 12621599669 / 10000000000, 2222804973 / 5000000000]
m : [1372958801 / 2500000000, -455084233 / 2000000000, 13019179717 / 10000000000]
j : [3992810119 / 5000000000, 1331325481 / 2000000000, -3569762671 / 10000000000]
h : [1904857711 / 5000000000, 7547931887 / 10000000000, 1219929729 / 1000000000]
o : [161564821 / 125000000, -1977620289 / 10000000000, -2544843721 / 10000000000]
p : [1016112907 / 1000000000, -7083058833 / 10000000000, 2798649473 / 5000000000]
c : [1796866933 / 10000000000, 8643295973 / 5000000000, 111471847 / 100000000]
k : [3611359507 / 10000000000, -547905231 / 5000000000, 493580267 / 5000000000]
n : [193137177 / 200000000, 2904094783 / 10000000000, 1109510769 / 2000000000]
d : [4984614023 / 10000000000, 4435415497 / 2000000000, 3027984041 / 10000000000]
b : [-2733072213 / 5000000000, 10520390381 / 10000000000, 9935911671 / 10000000000]
e : [1572280083 / 5000000000, 15391631789 / 10000000000, -510426277 / 1250000000]
l : [43322919 / 1250000000, -8385882113 / 10000000000, 3501739691 / 5000000000]
f : [-420953893 / 10000000000, 401486853 / 500000000, 1668947299 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 6493723795335444847848622859193552999711493336681209532041 / 15347454718214568750836456308390926038862500000000000000000
Collision distance in [65047217 / 100000000, 32523609 / 50000000] ~ [0.65047, 0.65047]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [467 / 1250, 1869 / 5000] ~ [0.3736, 0.3738]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 17564785840036900854896973 / 5000000000000000000000000000000000000000
rho in [592702047 / 10000000000000000, 692702047 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [436178 / 335410197, 3493161 / 2683281572] ~ [0.0013, 0.0013]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-383 / 2000000, 5249 / 25000000] ~ [-0.00019, 0.00021]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-9575 / 2683281572, 5249 / 1341640786] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [65047217 / 412310563, 10841203 / 68718427] ~ [0.15776, 0.15776]
Success: LHS < CD / |V| ^ .5
Success: existence proven