show/hide visualization coordinates
a : (-0.512964718425, -0.4787406499850001, -0.50666765824)
b : (-1.286598836425, 0.009771159014999864, -0.10312525933999994)
c : (-0.449875186425, 0.5047939109149999, -0.33731749854000004)
d : (0.29836384317500003, 0.02782680531499987, -0.79844734124)
e : (0.39892807777500006, -0.8287164236850001, -0.29226503183999997)
f : (-0.40808543352499993, -1.2480865465850002, 0.12349678745999998)
g : (-1.3179146884250001, -0.9852590986850002, -0.19764563873999996)
h : (-0.9424868547249999, -0.573453755885, 0.63269784576)
i : (-1.499778971825, 0.2281480233149999, 0.84916974496)
j : (-1.1410480511249999, 0.9370209922149999, 0.24187143326000002)
k : (-0.177928745025, 1.187027750915, 0.34135924296)
l : (0.456186003075, 0.9251111617149999, -0.38616957974)
m : (1.111150264375, 0.5555144819149999, -1.04527511674)
n : (1.2092685164749999, -0.34690987238500015, -0.6257478928400001)
o : (1.021692624675, -0.38997930138500014, 0.35555751816000003)
p : (0.052545769175000034, -0.4879346926850001, 0.58174132286)
q : (-0.5126360795249999, 0.3250164510149999, 0.72202644506)
r : (0.45232084527500005, 0.4228500924149999, 0.47853781496000003)
s : (1.290232295275, 0.4768312216149999, -0.06459240964000001)
t : (1.958629326175, -0.2608317090850001, 0.030795271459999995)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['n', 'm', 's'], ['a', 'e', 'f'], ['n', 't', 'o'], ['e', 'o', 'p'], ['k', 'r', 'q'], ['a', 'c', 'd'], ['b', 'c', 'j'], ['a', 'f', 'g'], ['o', 'r', 'p'], ['k', 'q', 'j'], ['i', 'q', 'j'], ['k', 'c', 'j'], ['a', 'e', 'd'], ['a', 'b', 'c'], ['b', 'i', 'j'], ['d', 'c', 'l'], ['p', 'q', 'h'], ['k', 'c', 'l'], ['e', 'n', 'o'], ['r', 's', 'l'], ['r', 'q', 'p'], ['e', 'f', 'p'], ['l', 'm', 'd'], ['f', 'g', 'h'], ['i', 'q', 'h'], ['k', 'r', 'l'], ['o', 'r', 's'], ['a', 'b', 'g'], ['e', 'n', 'd'], ['b', 'h', 'g'], ['m', 's', 'l'], ['h', 'f', 'p'], ['n', 't', 's'], ['o', 't', 's'], ['n', 'm', 'd'], ['b', 'i', 'h']]
Coordinate Data:
o : [-2593549977 / 5000000000, 4222264921 / 5000000000, 601090633 / 5000000000]
d : [2046187861 / 10000000000, 170658751 / 400000000, 637111493 / 500000000]
p : [4504368601 / 10000000000, 1884816751 / 2000000000, -1059656781 / 10000000000]
t : [-14556466969 / 10000000000, 7153053919 / 10000000000, 4449803733 / 10000000000]
l : [233983131 / 5000000000, -4706374789 / 10000000000, 1723890449 / 2000000000]
g : [18208973177 / 10000000000, 2879465563 / 2000000000, 1346842567 / 2000000000]
j : [4110076701 / 2500000000, -2412736547 / 5000000000, 467808423 / 2000000000]
m : [-6081676351 / 10000000000, -1010407991 / 10000000000, 3042101523 / 2000000000]
k : [6809113743 / 10000000000, -7325540681 / 10000000000, 672082009 / 5000000000]
i : [20027616011 / 10000000000, 452651319 / 2000000000, -1866970501 / 5000000000]
r : [6332723 / 125000000, 2470593 / 78125000, -13810851 / 5000000000]
s : [-393624833 / 500000000, -55893847 / 2500000000, 168865017 / 312500000]
b : [17895814657 / 10000000000, 2223512619 / 5000000000, 5789009041 / 10000000000]
e : [208109103 / 2000000000, 2566380213 / 2000000000, 3840203383 / 5000000000]
a : [10159473477 / 10000000000, 291629479 / 312500000, 982443303 / 1000000000]
f : [2277670157 / 2500000000, 8512801147 / 5000000000, 3522788573 / 10000000000]
c : [9528578157 / 10000000000, -503202281 / 10000000000, 8130931433 / 10000000000]
n : [-882857359 / 1250000000, 250432361 / 312500000, 688452211 / 625000000]
q : [634761693 / 625000000, 647286159 / 5000000000, -2462508003 / 10000000000]
h : [361367371 / 250000000, 10279274387 / 10000000000, -156922201 / 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 = 39859693868604186748330988532427165314628881194423611401 / 79719387795544812150746821166503016937500000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [643 / 1250, 2573 / 5000] ~ [0.5144, 0.5146]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1475677063066775609220083 / 10000000000000000000000000000000000000000
rho in [121477449 / 10000000000000000, 221477449 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [1653796 / 734846923, 6620329 / 2939387688] ~ [0.00225, 0.00225]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9931 / 50000000, 10127 / 50000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-9931 / 2939387688, 10127 / 2939387688] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [35355339 / 223606798, 70710679 / 447213595] ~ [0.15811, 0.15811]
Success: LHS < CD / |V| ^ .5
Success: existence proven