show/hide visualization coordinates
a : (1.1536338517, -0.5096740548100002, 0.27110486051499993)
b : (0.19374149890000003, -0.6811024021100002, 0.04925132091499995)
c : (0.7857952471000001, -0.22220926591000018, -0.613235998785)
d : (1.1811192365999998, 0.4546298601899998, 0.007737221714999909)
e : (0.9978443645, 0.2007259153899999, 0.957444075515)
f : (0.4900931557, -0.6595142963100001, 1.0040862017149998)
g : (-0.48479181279999994, -0.6371382386100002, 0.782504140515)
h : (-0.7776371822999999, -0.7913848980100002, -0.16113220748500007)
i : (-0.14384168199999992, -0.48511396391000017, -0.871414811885)
j : (0.2968613146000001, 0.29480660398999986, -1.315829906985)
k : (1.179711566, 0.62134410009, -0.9782670280850001)
l : (0.3500092224000001, 0.7801653659899999, -0.44313169348500003)
m : (0.4883912977000001, 0.9491085936899999, 0.532731302515)
n : (-0.001296828699999919, 0.21140030958999984, 0.997480725815)
o : (-0.9942819858999999, 0.21786315698999986, 0.879418415615)
p : (-1.4566087651, -0.6049729126100002, 0.5489721240149998)
q : (-1.195747564, 0.11457276128999988, -0.09461583168500004)
r : (-1.1270736324, -0.34045031401000014, -0.982443456785)
s : (-0.5290040531, 0.4320247527899998, -0.768913483685)
t : (-0.4069172488999999, 0.6549189262899999, 0.19825403001499997)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['t', 'm', 'l'], ['k', 'c', 'j'], ['g', 'p', 'h'], ['d', 'm', 'l'], ['g', 'o', 'n'], ['t', 's', 'l'], ['h', 'r', 'q'], ['t', 's', 'q'], ['d', 'c', 'k'], ['t', 'o', 'n'], ['s', 'i', 'j'], ['e', 'n', 'm'], ['e', 'd', 'a'], ['h', 'b', 'i'], ['h', 'r', 'i'], ['s', 'r', 'i'], ['t', 'o', 'q'], ['b', 'a', 'f'], ['e', 'n', 'f'], ['s', 'j', 'l'], ['c', 'j', 'i'], ['k', 'j', 'l'], ['g', 'n', 'f'], ['g', 'o', 'p'], ['e', 'd', 'm'], ['g', 'b', 'f'], ['e', 'a', 'f'], ['g', 'h', 'b'], ['b', 'c', 'a'], ['t', 'n', 'm'], ['o', 'p', 'q'], ['r', 's', 'q'], ['d', 'c', 'a'], ['d', 'k', 'l'], ['b', 'i', 'c'], ['p', 'h', 'q']]
Coordinate Data:
s : [6181939 / 1250000000, 4633712697 / 5000000000, -915680751 / 5000000000]
d : [17150688409 / 10000000000, 2373369117 / 2500000000, 370946597 / 625000000]
p : [-1153323951 / 1250000000, -55127563 / 500000000, 453899783 / 400000000]
m : [511170451 / 500000000, 14438263803 / 10000000000, 279627159 / 250000000]
q : [-6617979597 / 10000000000, 6092905479 / 10000000000, 2455807509 / 5000000000]
e : [1914742461 / 1250000000, 347721851 / 500000000, 1543221409 / 1000000000]
h : [-121843789 / 500000000, -1483335557 / 5000000000, 212322563 / 500000000]
f : [25601069 / 25000000, -1647965097 / 10000000000, 1987329419 / 1250000000]
n : [1331631939 / 2500000000, 3530590481 / 5000000000, 15832580593 / 10000000000]
a : [52736983 / 31250000, -74781341 / 5000000000, 428441097 / 500000000]
g : [98315583 / 2000000000, -35605113 / 250000000, 684140737 / 500000000]
b : [909613879 / 1250000000, -372769231 / 2000000000, 396892909 / 625000000]
l : [8839588267 / 10000000000, 6374415763 / 5000000000, 3566141 / 25000000]
r : [-5931240281 / 10000000000, 771337363 / 5000000000, -3966661233 / 10000000000]
t : [635161777 / 5000000000, 11496367129 / 10000000000, 1568062727 / 2000000000]
c : [6598724257 / 5000000000, 2725085207 / 10000000000, -274586653 / 10000000000]
j : [8308109189 / 10000000000, 3947621953 / 5000000000, -1460105147 / 2000000000]
o : [-575415477 / 1250000000, 1781452359 / 2500000000, 14651957491 / 10000000000]
i : [3901079223 / 10000000000, 96038227 / 10000000000, -5578857 / 19531250]
k : [17136611703 / 10000000000, 11160618867 / 10000000000, -1962448473 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 135850184320340806441318913620543973841948154495469263088449 / 246875194525277393208060916238736547073900000000000000000000
Collision distance in [37090389 / 50000000, 74180779 / 100000000] ~ [0.74181, 0.74181]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [821 / 2000, 4107 / 10000] ~ [0.4105, 0.4107]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 24237584254674955950319 / 10000000000000000000000000000000000000000
rho in [31136849 / 20000000000000000, 231136849 / 20000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [16851025 / 11757550768, 1874161 / 1306394528] ~ [0.00143, 0.00143]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9989 / 50000000, 10083 / 50000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-9989 / 2939387688, 3361 / 979795896] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [37090389 / 223606798, 74180779 / 447213595] ~ [0.16587, 0.16587]
Success: LHS < CD / |V| ^ .5
Success: existence proven