show/hide visualization coordinates
a : (-1.2104132563684211, -0.16111348266315784, -0.3107812367263157)
b : (-0.6636947071684212, 0.6246585512368421, -0.6000235895263157)
c : (-0.2517864344684211, -0.28595401766315787, -0.5666121519263156)
d : (-0.716380447268421, -0.9787093625631578, -0.0150303943263157)
e : (-0.7019674330684211, -0.1539590942631579, 0.5502830229736844)
f : (-1.188575359668421, 0.6664782641368421, 0.2501242872736843)
g : (-1.662116272968421, 0.6717490658368421, -0.6306317641263157)
h : (-0.2194186687684211, 0.912916294136842, 0.24822535707368432)
i : (0.3260657711315789, 0.5271112186368421, -0.4958184383263157)
j : (0.743197842831579, -0.38088615966315786, -0.5350815939263156)
k : (0.1607791817315789, -1.188962048063158, -0.4467534461263157)
l : (0.13635366583157893, -0.6820596795631579, 0.4149039005736843)
m : (0.17703608793157893, 0.21818953223684212, 0.8483739652736844)
n : (-0.6734388282684212, 0.6761337104368421, 1.1071780348736844)
o : (0.7735747108315789, 0.8406261850368422, 0.34170416707368434)
p : (1.315291255331579, 0.4263061401368421, -0.38965216582631573)
q : (1.692758545531579, -0.4875781250631579, -0.24020654152631565)
r : (0.9884921313315789, -1.106114802663158, 0.10824890227368433)
s : (0.9742422155315789, -0.1388321896631579, 0.36154968497368434)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['r', 'j', 'q'], ['d', 'a', 'c'], ['b', 'g', 'f'], ['d', 'a', 'e'], ['l', 's', 'r'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['b', 'h', 'f'], ['j', 'i', 'p'], ['l', 'k', 'r'], ['m', 'h', 'o'], ['m', 'h', 'n'], ['d', 'k', 'c'], ['b', 'g', 'a'], ['s', 'p', 'o'], ['m', 'e', 'n'], ['j', 'i', 'c'], ['s', 'm', 'o'], ['h', 'n', 'f'], ['b', 'a', 'c'], ['b', 'i', 'c'], ['i', 'p', 'o'], ['e', 'n', 'f'], ['j', 'q', 'p'], ['r', 'k', 'j'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['l', 'm', 'e'], ['s', 'r', 'q'], ['i', 'h', 'o'], ['l', 's', 'm'], ['g', 'a', 'f'], ['s', 'q', 'p']]
Coordinate Data:
d : [12346879747 / 10000000000, 7512427257 / 5000000000, 974408641 / 2000000000]
c : [7700939619 / 10000000000, 1619460213 / 2000000000, 10387860781 / 10000000000]
n : [11917463557 / 10000000000, -190447027 / 1250000000, -6350041087 / 10000000000]
s : [-4559346881 / 10000000000, 1325216557 / 2000000000, 276560603 / 2500000000]
q : [-11744510181 / 10000000000, 10113542139 / 10000000000, 7123804677 / 10000000000]
p : [-7969837279 / 10000000000, 974699487 / 10000000000, 215456523 / 250000000]
i : [1922417563 / 10000000000, -16675649 / 5000000000, 1935984729 / 2000000000]
m : [682542879 / 2000000000, 1527932783 / 5000000000, -3762000391 / 10000000000]
a : [8643603919 / 5000000000, 1369779143 / 2000000000, 7829551629 / 10000000000]
b : [5910011173 / 5000000000, -63051539 / 625000000, 10721975157 / 10000000000]
r : [-4701846039 / 10000000000, 3259781783 / 2000000000, 3639250239 / 10000000000]
e : [2440549921 / 2000000000, 6777351831 / 10000000000, -97636371 / 1250000000]
j : [-1124451577 / 5000000000, 1809324497 / 2000000000, 10072555201 / 10000000000]
k : [3575283457 / 10000000000, 17127381369 / 10000000000, 9189273723 / 10000000000]
l : [477442327 / 1250000000, 3014589421 / 2500000000, 17896883 / 312500000]
h : [3688630981 / 5000000000, -3891402053 / 10000000000, 2239485691 / 10000000000]
f : [17068828871 / 10000000000, -1427021753 / 10000000000, 2220496389 / 10000000000]
g : [5451059501 / 2500000000, -147972977 / 1000000000, 11028056903 / 10000000000]
o : [-1276335917 / 5000000000, -1584250481 / 5000000000, 1304697591 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 1864111043953300356485669227420501640758730575398328464241 / 3899346125582397845255675915307710723753515625000000000000
Collision distance in [6914169 / 10000000, 69141691 / 100000000] ~ [0.69142, 0.69142]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5091 / 10000, 5093 / 10000] ~ [0.5091, 0.5093]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 5631706988153381690971 / 5000000000000000000000000000000000000000
rho in [6633077 / 6250000000000000, 69133077 / 6250000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [25918281 / 11426285488, 25938649 / 11426285472] ~ [0.00227, 0.00227]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19989 / 100000000, 161 / 800000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-6663 / 1904380912, 2875 / 816163248] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [13828338 / 87177979, 69141691 / 435889894] ~ [0.15862, 0.15862]
Success: LHS < CD / |V| ^ .5
Success: existence proven