show/hide visualization coordinates
a : (0.9432785137000002, -0.0014774603235294115, 0.27820484410588237)
b : (0.15989902849999998, -0.5599007361235294, 0.5511151351058825)
c : (0.9887284965, -0.9975769562235294, 0.20257354620588247)
d : (1.250899615, -0.4246932822235294, -0.5740026575941176)
e : (1.4995125475, 0.5216431619764705, -0.3675106614941176)
f : (0.7563807821000001, 0.9695935233764706, 0.12957650720588237)
g : (0.15041277849999996, 0.42712307957647055, 0.7114086104058825)
h : (-0.7047211637999999, -0.09090171932352942, 0.7313145935058825)
i : (-0.6281046735, -0.7178867945235294, -0.04393996399411759)
j : (0.29128626809999997, -0.6688268761235294, -0.4342134846941176)
k : (0.5489843734, 0.2875635528764706, -0.5717236059941175)
l : (-0.1910611627, 0.8092764114764707, -0.14728480309411757)
m : (-0.7261075056, 0.9080859934764706, 0.6917396765058825)
n : (-1.085952215, 0.3696892183764706, -0.07025815669411756)
o : (-1.5298856305, -0.44885436232352943, 0.29430943550588246)
p : (-1.3226098046, -0.3852186932235294, -0.6819012145941176)
q : (-0.4009402476, 0.0023619392764706038, -0.6994078003941175)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['f', 'k', 'l'], ['i', 'j', 'q'], ['h', 'o', 'i'], ['f', 'l', 'g'], ['d', 'e', 'a'], ['f', 'e', 'a'], ['k', 'l', 'q'], ['b', 'j', 'c'], ['l', 'n', 'q'], ['i', 'q', 'p'], ['d', 'c', 'a'], ['b', 'j', 'i'], ['h', 'm', 'n'], ['l', 'm', 'n'], ['i', 'o', 'p'], ['k', 'e', 'f'], ['d', 'e', 'k'], ['h', 'o', 'n'], ['b', 'c', 'a'], ['h', 'm', 'g'], ['o', 'n', 'p'], ['l', 'm', 'g'], ['b', 'g', 'a'], ['j', 'd', 'c'], ['j', 'k', 'q'], ['b', 'h', 'g'], ['q', 'n', 'p'], ['b', 'h', 'i'], ['d', 'k', 'j'], ['f', 'g', 'a']]
Coordinate Data:
c : [14313693959 / 10000000000, -5303050797 / 10000000000, 6176950329 / 10000000000]
n : [-1608278289 / 2500000000, 8369610949 / 10000000000, 34486333 / 100000000]
l : [2515797367 / 10000000000, 19946067 / 15625000, 669591709 / 2500000000]
b : [6025399279 / 10000000000, -231572149 / 2500000000, 4831183109 / 5000000000]
d : [2116925643 / 1250000000, 425785943 / 10000000000, -1588811709 / 10000000000]
h : [-655200661 / 2500000000, 940925393 / 2500000000, 5732180401 / 5000000000]
i : [-1854637741 / 10000000000, -125307459 / 500000000, 3711815227 / 10000000000]
e : [19421534469 / 10000000000, 1977830077 / 2000000000, 119027063 / 2500000000]
o : [-10872447311 / 10000000000, 92087571 / 5000000000, 3547154611 / 5000000000]
p : [-2199922263 / 2500000000, 820531833 / 10000000000, -2667797279 / 10000000000]
f : [2398043363 / 2000000000, 14368653999 / 10000000000, 5446979939 / 10000000000]
q : [208503259 / 5000000000, 2348169079 / 5000000000, -2842863137 / 10000000000]
k : [1239531591 / 1250000000, 3774177147 / 5000000000, -1566021193 / 10000000000]
m : [-1417333031 / 5000000000, 137535787 / 100000000, 691788227 / 625000000]
a : [13859194131 / 10000000000, 2328972081 / 5000000000, 1733315827 / 2500000000]
j : [293570867 / 400000000, -503887499 / 2500000000, -9545999 / 500000000]
g : [5930536779 / 10000000000, 8943949561 / 10000000000, 11265300971 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 122493767955259240298002395329074194209899753634441478152361 / 249906833736015440588874213514514446295800000000000000000000
Collision distance in [14002253 / 20000000, 35005633 / 50000000] ~ [0.70011, 0.70011]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5867 / 10000, 5869 / 10000] ~ [0.5867, 0.5869]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 25828438332768901770657 / 10000000000000000000000000000000000000000
rho in [40178071 / 25000000000000000, 290178071 / 25000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [34421689 / 10733126304, 34445161 / 10733126288] ~ [0.00321, 0.00321]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9993 / 50000000, 20107 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-9993 / 2683281572, 20107 / 5366563144] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70011265 / 412310563, 35005633 / 206155281] ~ [0.1698, 0.1698]
Success: LHS < CD / |V| ^ .5
Success: existence proven