show/hide visualization coordinates
a : (-0.29598466310000004, 0.9052608800666667, -0.20584008631666678)
b : (-1.0836707909, 0.7250071224666667, 0.3832771661833332)
c : (-0.3537201487000001, 1.3325492130666667, 0.6964299825833333)
d : (0.42302780269999996, 0.7447105084666666, 0.4703585383833332)
e : (0.45125317769999995, 0.2731774622666667, -0.4110380870166668)
f : (-0.2382506644000001, 0.4749172117666668, -1.1066569524166667)
g : (-1.0493120907, 0.3376763912666667, -0.5380232138166667)
h : (-0.7320704644000001, -0.20054253593333327, 0.24279567448333328)
i : (-0.35709981310000005, 0.37138393056666674, 0.9723826257833332)
j : (0.5745236043999998, 0.1759059235666668, 1.2787584316833331)
k : (0.9051146712999999, -0.12724454173333327, 0.3849970997833332)
l : (1.0585423362, -0.5131307247333332, -0.5247015995166667)
m : (0.40767709099999994, -0.27569169703333324, -1.2458098189166669)
n : (-0.4035904202000001, -0.41305002903333327, -0.6774985329166667)
o : (-0.3270681450000001, -1.0943974077333332, 0.05045070508333327)
p : (0.06305359199999994, -0.5116662722333333, 0.7633528429833332)
q : (0.6618560578, -1.0790244170333332, 0.1980738418833332)
r : (0.29571886739999986, -1.1258410180333334, -0.7313086179166668)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['e', 'k', 'l'], ['c', 'i', 'b'], ['e', 'a', 'f'], ['a', 'f', 'g'], ['e', 'm', 'f'], ['n', 'f', 'g'], ['q', 'p', 'o'], ['c', 'a', 'd'], ['q', 'p', 'k'], ['c', 'i', 'd'], ['q', 'k', 'l'], ['q', 'r', 'o'], ['l', 'm', 'r'], ['h', 'i', 'b'], ['h', 'n', 'o'], ['h', 'p', 'o'], ['l', 'q', 'r'], ['e', 'a', 'd'], ['h', 'n', 'g'], ['j', 'i', 'd'], ['h', 'g', 'b'], ['p', 'k', 'j'], ['h', 'p', 'i'], ['k', 'j', 'd'], ['n', 'r', 'o'], ['e', 'k', 'd'], ['n', 'm', 'f'], ['a', 'g', 'b'], ['e', 'm', 'l'], ['c', 'a', 'b'], ['p', 'j', 'i'], ['n', 'r', 'm']]
Coordinate Data:
k : [14360972257 / 10000000000, 4327990831 / 10000000000, 1075730851 / 1250000000]
l : [7947624453 / 5000000000, 469129001 / 10000000000, -98228037 / 2000000000]
c : [1772624057 / 10000000000, 18925928379 / 10000000000, 2930043909 / 2500000000]
i : [1738827413 / 10000000000, 4657137777 / 5000000000, 3619925517 / 2500000000]
n : [636960671 / 5000000000, 734967979 / 5000000000, -2019109519 / 10000000000]
a : [2349978913 / 10000000000, 14653045049 / 10000000000, 2697474947 / 10000000000]
f : [29273189 / 100000000, 5174804183 / 5000000000, -3155346857 / 5000000000]
r : [4133507109 / 5000000000, -1414493483 / 2500000000, -2557210369 / 10000000000]
b : [-1105376473 / 2000000000, 12850507473 / 10000000000, 536790467 / 625000000]
e : [9822357321 / 10000000000, 8332210871 / 10000000000, 32274747 / 500000000]
d : [9540103571 / 10000000000, 13047541333 / 10000000000, 4729730597 / 5000000000]
q : [5964193061 / 5000000000, -2594903961 / 5000000000, 6736614229 / 10000000000]
o : [1019572047 / 5000000000, -5343537829 / 10000000000, 5260382861 / 10000000000]
m : [4693298227 / 5000000000, 1421759639 / 5000000000, -7702222379 / 10000000000]
j : [2763765397 / 2500000000, 1839873871 / 2500000000, 17543460127 / 10000000000]
g : [-5183295363 / 10000000000, 8977200161 / 10000000000, -78044541 / 1250000000]
p : [742545183 / 1250000000, 241886763 / 5000000000, 154867553 / 125000000]
h : [-20108791 / 100000000, 3595010889 / 10000000000, 1436766511 / 2000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 8587186725261382029304531380768684220161886874782959775609 / 15334582726587700116510732356405431663850000000000000000000
Collision distance in [14966473 / 20000000, 37416183 / 50000000] ~ [0.74832, 0.74832]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [218 / 625, 349 / 1000] ~ [0.3488, 0.349]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 749017666911091700764197243 / 10000000000000000000000000000000000000000
rho in [273681871 / 1000000000000000, 283681871 / 1000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [190096 / 173205081, 3045025 / 2771281292] ~ [0.0011, 0.0011]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-7827 / 50000000, 24509 / 100000000] ~ [-0.00016, 0.00025]
LHS DEN := 8 * |E| ^ .5 in [692820323 / 12500000, 173205081 / 3125000] ~ [55.42563, 55.42563]
LHS := (LHS NUM) / (LHS DEN) in [-7827 / 2771281292, 24509 / 5542562584] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [74832365 / 424264069, 12472061 / 70710678] ~ [0.17638, 0.17638]
Success: LHS < CD / |V| ^ .5
Success: existence proven