show/hide visualization coordinates
a : (-0.7637465337999999, -0.9086150516705884, 0.34965213747058815)
b : (0.00018992480000012968, -0.3680127764705883, 0.7020018151705881)
c : (-0.9400660465999998, -0.06360976807058838, 0.8545060491705881)
d : (-1.099528797, -0.09916693787058839, -0.1320573424294118)
e : (-0.455557887, -0.7176875276705883, -0.5823169827294119)
f : (0.17276146830000005, -1.1297632709705883, 0.07753782637058815)
g : (0.9160780383, -0.5086873553705884, 0.32602354227058816)
h : (0.6184680322000001, 0.40953862722941164, 0.5873457482705882)
i : (-0.17564812649999995, 0.4868361978294117, 1.1901762184705882)
j : (-0.5038106078999999, 0.6056765067294116, 0.25306023477058814)
k : (-0.34732850149999994, 0.27196351982941164, -0.6765359064294119)
l : (-0.04301797239999994, -0.3363346489705883, -1.409590093729412)
m : (0.5118211516000001, -0.46440820547058825, -0.5875495153294119)
n : (1.1127372419000001, 0.26937361372941165, -0.2705888080294119)
o : (0.3199588297000001, 0.8783037733294117, -0.24400946312941185)
p : (0.12239180410000006, 1.2753879458294115, 0.6522558150705882)
q : (0.5542979818000001, 0.39920535802941165, -1.0899112752294118)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['j', 'o', 'k'], ['l', 'e', 'm'], ['f', 'b', 'a'], ['k', 'e', 'l'], ['i', 'j', 'p'], ['i', 'j', 'c'], ['d', 'e', 'a'], ['f', 'e', 'a'], ['k', 'l', 'q'], ['h', 'i', 'p'], ['b', 'f', 'g'], ['h', 'o', 'p'], ['b', 'i', 'c'], ['f', 'm', 'g'], ['m', 'n', 'g'], ['d', 'e', 'k'], ['h', 'o', 'n'], ['b', 'c', 'a'], ['q', 'm', 'n'], ['q', 'o', 'n'], ['j', 'd', 'c'], ['h', 'n', 'g'], ['f', 'e', 'm'], ['k', 'o', 'q'], ['b', 'h', 'g'], ['b', 'h', 'i'], ['d', 'k', 'j'], ['l', 'm', 'q'], ['d', 'c', 'a'], ['j', 'o', 'p']]
Coordinate Data:
c : [7509836547 / 5000000000, 1869532757 / 2500000000, -939879189 / 2500000000]
n : [-5508359791 / 10000000000, 414829721 / 1000000000, 936428977 / 1250000000]
l : [189037261 / 312500000, 10205379837 / 10000000000, 18881444673 / 10000000000]
b : [280855669 / 500000000, 1315270139 / 1250000000, -139654651 / 625000000]
e : [5087295749 / 5000000000, 876181789 / 625000000, 10608713563 / 10000000000]
d : [8307150299 / 5000000000, 3916851363 / 5000000000, 152652929 / 250000000]
i : [7375493893 / 10000000000, 1973671369 / 10000000000, -7116218449 / 10000000000]
p : [4395094587 / 10000000000, -5911846111 / 10000000000, -347402883 / 2000000000]
o : [2419424331 / 10000000000, -970502193 / 5000000000, 7225638367 / 10000000000]
h : [-282833847 / 5000000000, 109865883 / 400000000, -1087913747 / 10000000000]
f : [778279589 / 2000000000, 18139666057 / 10000000000, 125317671 / 312500000]
q : [7603281 / 1000000000, 2849979767 / 10000000000, 1960582061 / 1250000000]
k : [9092297643 / 10000000000, 4122398149 / 10000000000, 28877257 / 25000000]
m : [62600139 / 1250000000, 5743057701 / 5000000000, 10661038889 / 10000000000]
a : [6628238983 / 5000000000, 1991022983 / 1250000000, 1289022361 / 10000000000]
j : [10657118707 / 10000000000, 19631707 / 250000000, 563735347 / 2500000000]
g : [-708353551 / 2000000000, 11928906901 / 10000000000, 1525308313 / 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 = 551295781321744432167826915972994044379662000415037186303481 / 979220782130885221077142030615667459837900000000000000000000
Collision distance in [1500659 / 2000000, 75032951 / 100000000] ~ [0.75033, 0.75033]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [613 / 1250, 2453 / 5000] ~ [0.4904, 0.4906]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 129369896714904671456140231 / 10000000000000000000000000000000000000000
rho in [14217611 / 125000000000000, 15467611 / 125000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [751538 / 335410197, 6017209 / 2683281572] ~ [0.00224, 0.00224]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-4689 / 25000000, 4271 / 20000000] ~ [-0.00019, 0.00021]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-4689 / 1341640786, 21355 / 5366563144] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [75032950 / 412310563, 75032951 / 412310562] ~ [0.18198, 0.18198]
Success: LHS < CD / |V| ^ .5
Success: existence proven