show/hide visualization coordinates
a : (0.3186978656, 0.2926608977049999, -1.1520780296549997)
b : (-0.4913837815, 0.5179247983049999, -0.6107612091549999)
c : (0.4181096231, 0.7642573325049999, -0.27588506865499984)
d : (1.2237881138, 0.580370358905, -0.8389727620549998)
e : (0.9854484342000001, -0.3906854430950001, -0.8546197000549999)
f : (0.012779090400000026, -0.6209715561950001, -0.8843291882549998)
g : (-0.581119414, -0.03704016049500014, -1.437780804255)
h : (-0.9049769257, -0.3911453573950001, -0.5604406071549999)
i : (-1.1880423216, 0.3230844265049999, 0.07967641134500014)
j : (-0.3769466347, 0.854577062105, 0.3238881329450002)
k : (0.4910177172999999, 0.5202777785049999, 0.6911508081450002)
l : (1.0896924503, 0.08455441810499986, 0.019039420645000193)
m : (0.529592801, -0.7419849249950001, -0.03682735765499989)
n : (-0.3894607056, -1.1269547553950001, -0.12131926135499987)
o : (-1.0757355165, -0.6180932792950001, 0.3983795763450001)
p : (-0.7101155402, 0.13975923570499993, 0.9387327925450002)
q : (-0.19336901630000003, 0.9135362014049999, 1.3051236183450001)
r : (0.1328090502, -0.020224542895000086, 1.4524285442450002)
s : (0.8353664010999999, -0.4044324269950001, 0.8534314903450002)
t : (-0.1261516909, -0.6394700629950001, 0.7111631933450002)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'p', 'o'], ['h', 'i', 'b'], ['t', 'p', 'o'], ['q', 'r', 'p'], ['h', 'i', 'o'], ['q', 'r', 'k'], ['c', 'j', 'k'], ['c', 'j', 'b'], ['i', 'j', 'p'], ['m', 't', 's'], ['m', 'f', 'n'], ['f', 'e', 'a'], ['l', 'c', 'd'], ['l', 'm', 's'], ['n', 't', 'o'], ['e', 'd', 'a'], ['l', 'c', 'k'], ['c', 'b', 'a'], ['h', 'f', 'g'], ['l', 'm', 'e'], ['m', 't', 'n'], ['q', 'j', 'p'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['t', 'r', 'p'], ['r', 's', 'k'], ['g', 'f', 'a'], ['h', 'n', 'o'], ['m', 'f', 'e'], ['h', 'g', 'b'], ['l', 'e', 'd'], ['q', 'j', 'k'], ['i', 'j', 'b'], ['h', 'n', 'f'], ['t', 'r', 's'], ['l', 's', 'k']]
Coordinate Data:
k : [2628132343 / 2500000000, 10905368567 / 10000000000, 2575706851 / 2000000000]
t : [434083529 / 1000000000, -86513731 / 1250000000, 13078658107 / 10000000000]
e : [15456836541 / 10000000000, 1795736351 / 10000000000, -2579170827 / 10000000000]
s : [1395601621 / 1000000000, 103641657 / 625000000, 14501341077 / 10000000000]
g : [-208841941 / 10000000000, 5332189177 / 10000000000, -8410781869 / 10000000000]
q : [917165509 / 2500000000, 3709488199 / 2500000000, 19018262357 / 10000000000]
h : [-1723708529 / 5000000000, 223892151 / 1250000000, 181310051 / 5000000000]
c : [978344843 / 1000000000, 13345164107 / 10000000000, 3208175487 / 10000000000]
l : [8249638351 / 5000000000, 6548134963 / 10000000000, 307871019 / 500000000]
p : [-1498803203 / 10000000000, 7100183139 / 10000000000, 15354354099 / 10000000000]
j : [458221463 / 2500000000, 14248361403 / 10000000000, 9205907503 / 10000000000]
i : [-6278071017 / 10000000000, 8933435047 / 10000000000, 6763790287 / 10000000000]
a : [1757866171 / 2000000000, 8629199759 / 10000000000, -5553754123 / 10000000000]
b : [43032149 / 625000000, 2176367753 / 2000000000, -70292959 / 5000000000]
f : [5730143103 / 10000000000, -25356239 / 500000000, -2876265709 / 10000000000]
m : [10898280209 / 10000000000, -429314617 / 2500000000, 5598752597 / 10000000000]
d : [17840233337 / 10000000000, 11506294371 / 10000000000, -2422701447 / 10000000000]
o : [-2577501483 / 5000000000, -478342011 / 10000000000, 9950821937 / 10000000000]
r : [6930442701 / 10000000000, 5500345353 / 10000000000, 40022093 / 19531250]
n : [1707745143 / 10000000000, -1391739193 / 2500000000, 118845839 / 250000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 826219542092630319687316561618037648235045085060571689729 / 1334316972844524278094321140751382194500000000000000000000
Collision distance in [491811 / 625000, 78689761 / 100000000] ~ [0.7869, 0.7869]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1369 / 2500, 2739 / 5000] ~ [0.5476, 0.5478]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 847987410428352054831 / 625000000000000000000000000000000000000
rho in [116480893 / 100000000000000000, 1116480893 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [1874161 / 734846923, 833569 / 326598632] ~ [0.00255, 0.00255]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-4997 / 25000000, 503 / 2500000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-4997 / 1469693844, 2515 / 734846922] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [19672440 / 111803399, 78689761 / 447213595] ~ [0.17596, 0.17596]
Success: LHS < CD / |V| ^ .5
Success: existence proven