show/hide visualization coordinates
a : (0.48672236254, 0.5259202770599999, -0.4497082700499999)
b : (0.89481696694, 1.1475114674599998, 0.21893453755000009)
c : (1.14825789794, 0.18016588315999993, 0.21574243605000004)
d : (1.00558007954, -0.30600594304000006, -0.64639443635)
e : (0.017253398140000042, -0.2856956986400001, -0.79738396725)
f : (-0.4979770767599999, 0.5531822851599999, -0.62182402005)
g : (-0.08918101976000004, 1.17799216396, 0.043381515450000074)
h : (0.29062453434, 0.4709478120599999, 0.6399014515500001)
i : (0.54181759234, -0.4969612990400001, 0.6325504740500001)
j : (1.36532570484, -0.7937095496400002, 0.14904774615000005)
k : (0.40566699114000004, -0.90055385144, -0.11102812154999997)
l : (-0.5818449847599999, -0.7461568307400002, -0.14235979945)
m : (-0.9738116034600001, -0.27062873714000013, -0.9299099183499999)
n : (-1.48380700386, 0.5777226706599999, -0.7877672203499999)
o : (-1.0813880231600002, 1.15783066316, -0.07957681674999995)
p : (-0.6690882320599999, 0.7375224090599999, 0.72872377335)
q : (-0.41972067976000005, -0.2304275294400001, 0.6989124429500001)
r : (-0.17127166815999995, -1.19782373174, 0.64974281285)
s : (0.79184084544, -1.4650986704400002, 0.6184641152500001)
t : (-0.97981608146, 0.16426620955999993, -0.029448735049999897)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'c', 'i'], ['c', 'j', 'd'], ['t', 'p', 'o'], ['c', 'i', 'j'], ['e', 'd', 'k'], ['h', 'p', 'g'], ['n', 'f', 'o'], ['l', 't', 'm'], ['m', 'f', 'n'], ['f', 'e', 'a'], ['l', 'r', 'k'], ['n', 't', 'o'], ['e', 'd', 'a'], ['h', 'q', 'p'], ['c', 'b', 'a'], ['h', 'q', 'i'], ['l', 'm', 'e'], ['m', 't', 'n'], ['s', 'j', 'k'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['o', 'p', 'g'], ['j', 'i', 's'], ['r', 'i', 's'], ['r', 's', 'k'], ['j', 'd', 'k'], ['h', 'c', 'b'], ['q', 'r', 'i'], ['g', 'f', 'a'], ['l', 'e', 'k'], ['m', 'f', 'e'], ['t', 'q', 'p'], ['l', 'q', 't'], ['h', 'g', 'b'], ['g', 'f', 'o'], ['l', 'q', 'r']]
Coordinate Data:
k : [1799247889 / 10000000000, 3556754537 / 2500000000, 1307335407 / 2000000000]
t : [3130815723 / 2000000000, 1789408769 / 5000000000, 572088317 / 1000000000]
e : [5683383819 / 10000000000, 403921831 / 500000000, 3350058873 / 2500000000]
s : [-1031245327 / 5000000000, 9936233169 / 5000000000, -758245333 / 10000000000]
g : [3373863999 / 5000000000, -3279221003 / 5000000000, 998516133 / 2000000000]
q : [5026562299 / 5000000000, 470359683 / 625000000, -156272861 / 1000000000]
h : [2949672457 / 10000000000, 512001513 / 10000000000, -121577337 / 1250000000]
c : [-5626661179 / 10000000000, 1709910401 / 5000000000, 3268971459 / 10000000000]
l : [364823989 / 312500000, 12683047941 / 10000000000, 3424996907 / 5000000000]
p : [12546800121 / 10000000000, -2153744457 / 10000000000, -930420957 / 5000000000]
j : [-487333703 / 625000000, 1315857513 / 1000000000, 1967959179 / 5000000000]
i : [437741877 / 10000000000, 636943289 / 625000000, -899108921 / 10000000000]
a : [39547767 / 400000000, -37723137 / 10000000000, 248086963 / 250000000]
b : [-3092251869 / 10000000000, -6253635041 / 10000000000, 809262611 / 2500000000]
f : [1354461071 / 1250000000, -155171609 / 5000000000, 582231801 / 500000000]
m : [3118806767 / 2000000000, 1585553401 / 2000000000, 14725495003 / 10000000000]
d : [-839976599 / 2000000000, 1035192383 / 1250000000, 11890340183 / 10000000000]
o : [1041862377 / 625000000, -3178413499 / 5000000000, 6222163987 / 10000000000]
r : [3784317241 / 5000000000, 17199716951 / 10000000000, -1071032309 / 10000000000]
n : [20693987839 / 10000000000, -555747073 / 10000000000, 13304068023 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 16637540954673397085187003001577708868894667035933180964761 / 39294211944965535731469297034722746582084000000000000000000
Collision distance in [406687 / 625000, 65069921 / 100000000] ~ [0.6507, 0.6507]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [3737 / 10000, 3739 / 10000] ~ [0.3737, 0.3739]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 105601016922756965153622107 / 5000000000000000000000000000000000000000
rho in [36331979 / 250000000000000, 38831979 / 250000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [13965169 / 11757550768, 13980121 / 11757550752] ~ [0.00119, 0.00119]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-3543 / 20000000, 5611 / 25000000] ~ [-0.00018, 0.00022]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-5905 / 1959591792, 5611 / 1469693844] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [16267480 / 111803399, 65069921 / 447213595] ~ [0.1455, 0.1455]
Success: LHS < CD / |V| ^ .5
Success: existence proven