show/hide visualization coordinates
a : (-0.5347337437923076, 0.8138944335153846, 0.4367198873153846)
b : (0.14383356720769236, 0.12874354221538453, 0.7015292216153847)
c : (0.4345382863076923, 1.0574546761153845, 0.4713473943153845)
d : (-0.031935534292307666, 0.9847901684153846, -0.41020224448461545)
e : (-0.35606313499230763, 0.06227082061538458, -0.19882645478461544)
f : (-0.8255266104923076, -0.11443687198461544, 0.6667017963153846)
g : (-0.14726569759230762, -0.7998994059846154, 0.9314867418153846)
h : (0.35591271060769236, -0.6289821987846155, 0.08437642001538459)
i : (0.6468102640076923, 0.2996987354153845, -0.14569685848461544)
j : (0.1800312585076923, 0.22734378811538458, -1.0271112006846155)
k : (-0.11075178909230765, -0.7009994208846154, -0.7971261987846154)
l : (-0.6135237068923076, -0.8718899721846154, 0.04976754911538456)
m : (0.8586741305076924, -0.45798829458461543, -0.7629660532846154)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['k', 'j', 'e'], ['b', 'g', 'f'], ['j', 'e', 'd'], ['k', 'h', 'l'], ['i', 'j', 'd'], ['g', 'h', 'l'], ['e', 'd', 'a'], ['m', 'k', 'h'], ['m', 'j', 'k'], ['b', 'h', 'i'], ['c', 'b', 'a'], ['b', 'f', 'a'], ['g', 'l', 'f'], ['c', 'b', 'i'], ['i', 'd', 'c'], ['b', 'g', 'h'], ['c', 'd', 'a'], ['m', 'h', 'i'], ['m', 'j', 'i'], ['f', 'e', 'a'], ['f', 'l', 'e'], ['k', 'l', 'e']]
Coordinate Data:
j : [283216201 / 400000000, 3789461961 / 5000000000, -5823914541 / 10000000000]
h : [4419609773 / 5000000000, -984335947 / 10000000000, 2645480833 / 5000000000]
i : [293704877 / 250000000, 1660494679 / 2000000000, 2990228881 / 10000000000]
e : [171946109 / 1000000000, 5928194247 / 10000000000, 1229466459 / 5000000000]
l : [-855144629 / 10000000000, -3413413681 / 10000000000, 4944872957 / 10000000000]
k : [4172574549 / 10000000000, -213063521 / 1250000000, -1762032261 / 5000000000]
a : [-33622499 / 5000000000, 1680553797 / 1250000000, 8814396339 / 10000000000]
c : [9625475303 / 10000000000, 7940016401 / 5000000000, 9160671409 / 10000000000]
b : [419901757 / 625000000, 6592921463 / 10000000000, 5731244841 / 5000000000]
m : [2773366749 / 2000000000, 145120619 / 2000000000, -3182463067 / 10000000000]
d : [4960737097 / 10000000000, 606135509 / 400000000, 345175021 / 10000000000]
g : [475929433 / 1250000000, -2693508019 / 10000000000, 3440516221 / 2500000000]
f : [-595034733 / 2000000000, 4161117321 / 10000000000, 11114215429 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 13
|E| = 33
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 73627210056288229545140133919981432671266215251223424929623 / 142826054536430842828669266677560709285300000000000000000000
Collision distance in [71798513 / 100000000, 35899257 / 50000000] ~ [0.71799, 0.71799]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [277 / 2000, 1387 / 10000] ~ [0.1385, 0.1387]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 66796663118426017832409503538889931 / 10000000000000000000000000000000000000000
rho in [5169 / 2000000, 258451 / 100000000] ~ [0.00258, 0.00258]
sigma_min ^ 2 / (16 * E ^ .5) in [383645 / 1838260048, 1923769 / 9191300224] ~ [0.00021, 0.00021]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)