show/hide visualization coordinates
a : (0.0022556478421053017, -1.0690926928263158, 0.38742787630526304)
b : (-0.6643378834578947, -0.5807831822263159, -0.17578335049473692)
c : (0.02984802584210533, -1.1560640836263159, -0.608400742394737)
d : (0.7899969967421053, -0.7241801081263157, -0.12296302889473698)
e : (0.5860517951421054, -0.36209521142631584, 0.786597789405263)
f : (-0.40063624655789465, -0.21518573062631585, 0.716853165605263)
g : (-1.1945449478578944, 0.15934077047368417, 0.23785538500526304)
h : (-0.8536651447578946, 0.25088422677368416, -0.6977838378947371)
i : (-0.5647088418578946, -0.5814333795263158, -1.170807787994737)
j : (0.31312861294210537, -0.22747509062631588, -0.8481393315947369)
k : (0.8100548318421054, 0.27545698987368417, -0.140945118294737)
l : (1.4931325000421054, -0.22892889512631587, 0.38725917750526306)
m : (1.0109157224421055, 0.5430406434736842, 0.8014209946052631)
n : (0.15466859954210538, 0.38450188857368417, 1.2930573719052632)
o : (-0.7069451527578946, 0.7170304469736841, 0.909590946205263)
p : (-0.7394316241578945, 1.0025661876736842, -0.04822634829473693)
q : (0.03417096544210535, 0.7017904706736842, -0.605965535994737)
r : (-0.2394431575578947, 0.3105878777736842, -1.484655380494737)
s : (0.13948930114210534, 0.8000388718736842, 0.383607755805263)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['r', 'j', 'q'], ['d', 'a', 'c'], ['b', 'g', 'f'], ['d', 'a', 'e'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['o', 'n', 'f'], ['k', 's', 'q'], ['s', 'n', 'o'], ['d', 'k', 'j'], ['h', 'p', 'q'], ['s', 'p', 'o'], ['m', 'e', 'n'], ['d', 'j', 'c'], ['j', 'i', 'c'], ['l', 'k', 'm'], ['s', 'm', 'n'], ['b', 'a', 'c'], ['b', 'i', 'c'], ['k', 'j', 'q'], ['r', 'i', 'j'], ['e', 'n', 'f'], ['r', 'h', 'i'], ['g', 'p', 'o'], ['o', 'g', 'f'], ['b', 'g', 'h'], ['a', 'e', 'f'], ['b', 'a', 'f'], ['b', 'i', 'h'], ['l', 'm', 'e'], ['g', 'h', 'p'], ['r', 'h', 'q'], ['k', 's', 'm'], ['s', 'q', 'p']]
Coordinate Data:
d : [-694922871 / 2500000000, 2692749437 / 2000000000, 1244630251 / 2000000000]
c : [192871929 / 400000000, 889129347 / 500000000, 1107752839 / 1000000000]
n : [446699061 / 1250000000, 1188463609 / 5000000000, -7937052753 / 10000000000]
s : [14552287 / 39062500, -355688523 / 2000000000, 72340213 / 625000000]
q : [4778568829 / 10000000000, -795958603 / 10000000000, 5526588163 / 5000000000]
p : [500583789 / 400000000, -3803715773 / 10000000000, 5475784449 / 10000000000]
i : [5383683451 / 5000000000, 12036279899 / 10000000000, 8350799423 / 5000000000]
m : [-4988878741 / 10000000000, 791539669 / 10000000000, -151034449 / 500000000]
a : [1019544401 / 2000000000, 2114109129 / 1250000000, 1119242203 / 10000000000]
b : [5881828659 / 5000000000, 6014888963 / 5000000000, 6751354471 / 10000000000]
r : [7514710059 / 10000000000, 1558033663 / 5000000000, 19840074771 / 10000000000]
e : [-185059867 / 2500000000, 4921449109 / 5000000000, -89764279 / 312500000]
j : [994496177 / 5000000000, 849669701 / 1000000000, 6737457141 / 5000000000]
k : [-596053967 / 2000000000, 693475241 / 2000000000, 6402972149 / 10000000000]
l : [-9811046517 / 10000000000, 1702247011 / 2000000000, 1120929191 / 10000000000]
h : [13656929931 / 10000000000, 928275959 / 2500000000, 2394271869 / 2000000000]
f : [9126640949 / 10000000000, 837380341 / 1000000000, -217501069 / 1000000000]
g : [8532863981 / 5000000000, 4628538399 / 10000000000, 653741779 / 2500000000]
o : [12189730011 / 10000000000, -474179183 / 5000000000, -256399281 / 625000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 4947557769949420809066549488441391767044859816650927448647 / 8704285414445052369014003410213325300912500000000000000000
Collision distance in [37696313 / 50000000, 75392627 / 100000000] ~ [0.75393, 0.75393]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [4721 / 10000, 4723 / 10000] ~ [0.4721, 0.4723]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1535016438858071814097 / 1250000000000000000000000000000000000000
rho in [55407877 / 50000000000000000, 555407877 / 50000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [22287841 / 11426285488, 22306729 / 11426285472] ~ [0.00195, 0.00195]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19987 / 100000000, 4027 / 20000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-19987 / 5713142736, 20135 / 5713142736] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [75392626 / 435889895, 75392627 / 435889894] ~ [0.17296, 0.17296]
Success: LHS < CD / |V| ^ .5
Success: existence proven