show/hide visualization coordinates
a : (-0.24126298524210527, -0.7428979159, 0.651900137431579)
b : (-0.4320614147421053, -0.6170280026000001, -0.32162578466842096)
c : (0.35096951365789475, -1.1678357409, -0.03270815736842092)
d : (0.5591720720578948, -1.268438286, 0.940189996631579)
e : (0.48735855605789474, -0.2986114698000001, 1.173168023031579)
f : (-0.25326274224210527, 0.24840276309999992, 0.782968697031579)
g : (-1.0365947044421053, -0.2099506939000001, 0.36308405743157907)
h : (-1.1751026745421054, -0.011794073400000049, -0.6072506629684209)
i : (-0.24044225924210522, 0.16360476939999996, -0.9165161718684209)
j : (0.49085174575789475, -0.23419254030000003, -0.36247070386842095)
k : (1.0435101286578947, -0.5856212269000001, 0.3932187775315791)
l : (1.2256564201578948, -1.5589288310000002, 0.2535941498315791)
m : (0.6779657017578947, 0.3443892184999999, 0.43140051713157906)
n : (0.05832532425789477, 1.1292603576, 0.42659425763157904)
o : (-0.6863153895421052, 0.6409402777, -0.028437322668420917)
p : (-0.9279813708421054, 0.8880078791999999, -0.966816341668421)
q : (-0.0006240885421052722, 1.0546882196, -1.301818038568421)
r : (0.40325243435789476, 0.759243935, -0.436025667668421)
s : (-0.30341426734210525, 1.4667613606, -0.44244976236842093)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'q', 'p'], ['h', 'p', 'o'], ['s', 'q', 'p'], ['d', 'a', 'c'], ['d', 'a', 'e'], ['d', 'k', 'l'], ['o', 'n', 'f'], ['s', 'r', 'n'], ['d', 'k', 'e'], ['m', 'n', 'f'], ['r', 'i', 'q'], ['s', 'n', 'o'], ['b', 'j', 'i'], ['l', 'k', 'c'], ['b', 'g', 'a'], ['r', 'j', 'm'], ['r', 'm', 'n'], ['s', 'p', 'o'], ['b', 'a', 'c'], ['r', 'i', 'j'], ['l', 'd', 'c'], ['b', 'j', 'c'], ['g', 'h', 'o'], ['o', 'g', 'f'], ['b', 'g', 'h'], ['i', 'h', 'p'], ['m', 'e', 'f'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['m', 'k', 'e'], ['s', 'r', 'q'], ['g', 'a', 'f'], ['k', 'j', 'm']]
Coordinate Data:
d : [-1760047061 / 10000000000, 18196790481 / 10000000000, -4246421793 / 10000000000]
c : [321978523 / 10000000000, 1719076503 / 1000000000, 5482559747 / 10000000000]
n : [3248420417 / 10000000000, -1156039191 / 2000000000, 889535597 / 10000000000]
s : [6865816333 / 10000000000, -1831041197 / 2000000000, 9579975797 / 10000000000]
q : [767582909 / 2000000000, -201378983 / 400000000, 18173658559 / 10000000000]
p : [1638935921 / 1250000000, -3367671171 / 10000000000, 1482364159 / 1000000000]
i : [1559024063 / 2500000000, 3876359927 / 10000000000, 3580159973 / 2500000000]
m : [-1473991679 / 5000000000, 517128859 / 2500000000, 420736501 / 5000000000]
a : [780537939 / 1250000000, 647069339 / 500000000, -1363523201 / 10000000000]
b : [8152287807 / 10000000000, 11682687647 / 10000000000, 418586801 / 500000000]
e : [-1041911901 / 10000000000, 8498522319 / 10000000000, -6576202057 / 10000000000]
r : [-50212671 / 2500000000, -2080031729 / 10000000000, 190314697 / 200000000]
j : [-538421899 / 5000000000, 245447907 / 312500000, 2195046303 / 2500000000]
k : [-6603427627 / 10000000000, 1136861989 / 1000000000, 611645199 / 5000000000]
l : [-4212445271 / 5000000000, 21101695931 / 10000000000, 104781467 / 400000000]
h : [3116540081 / 2000000000, 1126069671 / 2000000000, 11227984803 / 10000000000]
f : [3182150541 / 5000000000, 302837999 / 1000000000, -2674208797 / 10000000000]
g : [443675647 / 312500000, 23787233 / 31250000, 1524637599 / 10000000000]
o : [2138965511 / 2000000000, -224248789 / 2500000000, 27199257 / 50000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 499999999426279594420220601012858317558666264800096755063601 / 1000000004427327535029088827706483808157100000000000000000000
Collision distance in [70710677 / 100000000, 35355339 / 50000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [899 / 2500, 1799 / 5000] ~ [0.3596, 0.3598]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 118584741756887311497761677 / 10000000000000000000000000000000000000000
rho in [108896621 / 1000000000000000, 118896621 / 1000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [808201 / 714142843, 462343 / 408081624] ~ [0.00113, 0.00113]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-18271 / 100000000, 2189 / 10000000] ~ [-0.00018, 0.00022]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-18271 / 5713142736, 10945 / 2856571368] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710677 / 435889895, 35355339 / 217944947] ~ [0.16222, 0.16222]
Success: LHS < CD / |V| ^ .5
Success: existence proven