show/hide visualization coordinates
a : (0.8715560749777778, 0.48920773783333327, -0.4208479009166667)
b : (1.0286461255777777, -0.2816618694666667, 0.19647111248333338)
c : (1.4360119583777777, -0.2813800352666668, -0.7167939086166667)
d : (0.5319153367777777, -0.13991346096666668, -1.1200264804166666)
e : (-0.10322138532222225, 0.46755898233333326, -0.6429745181166667)
f : (0.25121883157777775, 1.1603455045333333, -0.014946678616666653)
g : (0.8680638205777778, 0.6324261666333333, 0.5688370416833334)
h : (0.5227452054777777, -0.1720840701666667, 1.0520743877833334)
i : (0.13981654567777774, -0.7250725927666667, 0.31209510758333336)
j : (0.6890053872777777, -0.9107830684666668, -0.5027074669166666)
k : (-0.22824933892222232, -0.5234617582666667, -0.5955835669166666)
l : (-1.006491808722222, 0.08640877843333328, -0.4459286751166667)
m : (-0.7264618069222223, 0.9506550343333333, -0.02800331441666659)
n : (-0.10961681782222232, 0.42273569653333326, 0.5557804057833333)
o : (-0.4549354330222223, -0.3817745404666667, 1.0390177519833332)
p : (-0.8494017581222223, -0.6844608289666668, 0.17139033838333334)
q : (-1.7733034810222223, -0.3217909020666667, 0.0494225942833334)
r : (-1.0872974564222222, 0.21304522623333327, 0.5427237700833334)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['e', 'd', 'a'], ['l', 'e', 'm'], ['b', 'c', 'a'], ['l', 'r', 'q'], ['j', 'b', 'c'], ['f', 'm', 'e'], ['m', 'r', 'n'], ['f', 'g', 'n'], ['i', 'j', 'k'], ['r', 'q', 'p'], ['j', 'd', 'k'], ['l', 'e', 'k'], ['h', 'o', 'n'], ['b', 'a', 'g'], ['m', 'f', 'n'], ['d', 'c', 'a'], ['h', 'b', 'g'], ['h', 'i', 'b'], ['e', 'd', 'k'], ['i', 'j', 'b'], ['h', 'g', 'n'], ['l', 'r', 'm'], ['o', 'r', 'p'], ['p', 'l', 'k'], ['f', 'e', 'a'], ['i', 'k', 'p'], ['l', 'q', 'p'], ['f', 'a', 'g'], ['h', 'o', 'i'], ['i', 'o', 'p'], ['j', 'd', 'c'], ['o', 'r', 'n']]
Coordinate Data:
q : [23634493361 / 10000000000, 7734173927 / 10000000000, 1004917291 / 2000000000]
f : [677854047 / 2000000000, -7087190139 / 10000000000, 354267449 / 625000000]
i : [2251646547 / 5000000000, 5883495417 / 5000000000, 1198930661 / 5000000000]
h : [21062703 / 312500000, 779638201 / 1250000000, -125048287 / 250000000]
d : [582305183 / 10000000000, 1478849879 / 2500000000, 8359538601 / 5000000000]
l : [7983188319 / 5000000000, 1826088561 / 5000000000, 9978099149 / 10000000000]
m : [658303831 / 500000000, -4990285437 / 10000000000, 2899422771 / 5000000000]
j : [-494297661 / 5000000000, 13624095591 / 10000000000, 10545887067 / 10000000000]
a : [-2814102199 / 10000000000, -46976559 / 1250000000, 9727291407 / 10000000000]
o : [10450812881 / 10000000000, 8334010311 / 10000000000, -2435682561 / 5000000000]
e : [1733418101 / 2500000000, -159324917 / 10000000000, 11948557579 / 10000000000]
c : [-8458661033 / 10000000000, 7330065259 / 10000000000, 3171687871 / 2500000000]
n : [6997626729 / 10000000000, 288907941 / 10000000000, -1949583 / 500000000]
p : [3598869033 / 2500000000, 2840218299 / 2500000000, 1902454507 / 5000000000]
g : [-555835931 / 2000000000, -45199919 / 250000000, -169558019 / 10000000000]
k : [409197597 / 500000000, 9750882489 / 10000000000, 11474648067 / 10000000000]
b : [-877000541 / 2000000000, 7332883601 / 10000000000, 3554101273 / 10000000000]
r : [3354886623 / 2000000000, 596453161 / 2500000000, 91574697 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 166666666666275948646268613521445396270568747039175792488827 / 333333333355880151999587896289861048647400000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1317 / 10000, 1319 / 10000] ~ [0.1317, 0.1319]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 13806780379344060126757 / 10000000000000000000000000000000000000000
rho in [7343891 / 6250000000000000, 69843891 / 6250000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [192721 / 1231680576, 1739761 / 11085125168] ~ [0.00016, 0.00016]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19951 / 100000000, 20471 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [692820323 / 12500000, 173205081 / 3125000] ~ [55.42563, 55.42563]
LHS := (LHS NUM) / (LHS DEN) in [-19951 / 5542562584, 20471 / 5542562584] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710678 / 424264069, 70710679 / 424264068] ~ [0.16667, 0.16667]
Success: LHS < CD / |V| ^ .5
Success: existence proven