show/hide visualization coordinates
a : (0.5360969586, -0.6409994897210527, -0.7126954008999999)
b : (0.7560106573, -0.5410477418210526, 0.25768989020000005)
c : (0.5560184957000001, -1.4455054717210527, -0.11908504279999998)
d : (-0.3195073648, -1.0704015061210526, -0.42363632349999997)
e : (-0.32455105230000003, -0.13637455942105264, -0.7808032645999999)
f : (0.4781553409, 0.1730098493789473, -1.2906500397)
g : (0.8161315118999999, 0.2488779785789474, -0.352558288)
h : (0.9424937352, 0.3671678011789474, 0.6323478529)
i : (0.06314268270000001, -0.07534688722105265, 0.8081957337000001)
j : (-0.06778092260000002, -1.0307078444210527, 0.5433477568)
k : (-0.29712926900000003, -1.9081263802210526, 0.12199748790000003)
l : (-0.6475352334, -0.31828318752105267, 0.14795422230000005)
m : (-0.8790747372000001, 0.5442394195789473, -0.30198378499999995)
n : (0.0275442427, 0.7897117791789472, -0.645182482)
o : (0.632432629, 1.1353489322789474, 0.07220513880000007)
p : (0.15721376199999992, 0.9135019136789473, 0.923645641)
q : (-0.7310652412, 0.5200302796789473, 0.6867058057)
r : (-1.3428011215, 1.2040318305789472, 0.2893129383)
s : (-0.355795074, 1.2708732840789474, 0.1431921589000001)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'q', 'p'], ['h', 'p', 'o'], ['d', 'a', 'c'], ['d', 'a', 'e'], ['l', 'i', 'q'], ['d', 'e', 'l'], ['d', 'j', 'l'], ['s', 'n', 'o'], ['d', 'k', 'j'], ['d', 'k', 'c'], ['b', 'j', 'i'], ['b', 'g', 'a'], ['m', 'e', 'n'], ['s', 'r', 'm'], ['s', 'p', 'o'], ['l', 'm', 'q'], ['s', 'm', 'n'], ['b', 'a', 'c'], ['g', 'n', 'o'], ['e', 'n', 'f'], ['b', 'j', 'c'], ['g', 'n', 'f'], ['g', 'h', 'o'], ['l', 'i', 'j'], ['b', 'g', 'h'], ['i', 'h', 'p'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['l', 'm', 'e'], ['s', 'r', 'q'], ['r', 'm', 'q'], ['g', 'a', 'f'], ['s', 'q', 'p']]
Coordinate Data:
d : [184899541 / 1000000000, -6084333309 / 10000000000, 295241181 / 5000000000]
c : [2120850803 / 2000000000, -1967074593 / 2000000000, 3635995169 / 10000000000]
n : [1063902297 / 2000000000, 1564599943 / 1250000000, -1624979223 / 10000000000]
s : [743059159 / 5000000000, 17328414593 / 10000000000, 3129383593 / 5000000000]
q : [-1133291677 / 5000000000, 9819984549 / 10000000000, 5846951827 / 5000000000]
p : [3308103339 / 5000000000, 13754700889 / 10000000000, 14063302007 / 10000000000]
i : [1135099177 / 2000000000, 48327661 / 125000000, 6454401467 / 5000000000]
m : [-1873339157 / 5000000000, 2515518987 / 2500000000, 1807007747 / 10000000000]
a : [2601259661 / 2500000000, -358062629 / 2000000000, -575027103 / 2500000000]
b : [12604175631 / 10000000000, -395397833 / 5000000000, 7403744499 / 10000000000]
e : [359711707 / 2000000000, 1627968079 / 5000000000, -2981187049 / 10000000000]
r : [-8383942157 / 10000000000, 8330000029 / 5000000000, 385998749 / 500000000]
j : [545782479 / 1250000000, -1421849173 / 2500000000, 2052064633 / 2000000000]
k : [129548523 / 625000000, -289231641 / 200000000, 1511705119 / 2500000000]
l : [-357820819 / 2500000000, 1436849877 / 10000000000, 315319391 / 500000000]
h : [1446900641 / 1000000000, 2072839941 / 2500000000, 5575162063 / 5000000000]
f : [9825622467 / 10000000000, 3174890123 / 5000000000, -20199137 / 25000000]
g : [13205384177 / 10000000000, 3554230769 / 5000000000, 1301262717 / 10000000000]
o : [2842098837 / 2500000000, 638926843 / 400000000, 1109779397 / 2000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 499999999990652718319547491791609949158422125641972217341649 / 1000000000053054217902353812985691067238500000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [6101 / 10000, 6103 / 10000] ~ [0.6101, 0.6103]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 5577303923026961515193 / 5000000000000000000000000000000000000000
rho in [6600961 / 6250000000000000, 69100961 / 6250000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [37222201 / 11426285488, 37246609 / 11426285472] ~ [0.00326, 0.00326]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19991 / 100000000, 2513 / 12500000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-19991 / 5713142736, 359 / 102020406] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710678 / 435889895, 70710679 / 435889894] ~ [0.16222, 0.16222]
Success: LHS < CD / |V| ^ .5
Success: existence proven