show/hide visualization coordinates
a : (-0.384638404136842, 0.6854377164421053, -0.10724468096842099)
b : (-0.517163320436842, 0.5771115565421053, 0.877997720331579)
c : (0.251669113363158, 1.1155932462421052, 0.533129399631579)
d : (0.588508469163158, 0.7408723208421053, -0.330654992568421)
e : (-0.04884289033684197, 0.31682779684210527, -0.974059597768421)
f : (-1.017241017536842, 0.2361293596421053, -0.738066315068421)
g : (-1.047367754436842, 0.020931298342105276, 0.23803930123157896)
h : (-0.363891608736842, -0.40977652735789466, 0.8274043213315789)
i : (0.412370252863158, 0.2121383788421053, 0.930551651631579)
j : (1.161961570063158, 0.7041213285421053, 0.48775865933157897)
k : (1.160653535363158, -0.06059871325789473, -0.15660268846842107)
l : (0.936741634663158, 0.1994305730421053, -1.095883387268421)
m : (0.402608508663158, -0.5072445310578948, -0.6318660374684211)
n : (-0.5076847385368419, -0.5691517182578947, -1.041174850368421)
o : (-1.296186459336842, -0.6752195406578947, -0.43535750716842103)
p : (-1.160504280436842, -0.9312864557578946, 0.521731872731579)
q : (-0.37183838213684206, -0.8225444113578946, -0.08339726106842105)
r : (0.497973593463158, -0.6038636342578947, 0.358876234531579)
s : (1.3028721784631578, -0.22890804335789466, 0.8188181574315789)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['q', 'p', 'o'], ['d', 'a', 'c'], ['d', 'a', 'e'], ['k', 's', 'r'], ['o', 'n', 'q'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['o', 'n', 'f'], ['r', 's', 'i'], ['d', 'k', 'j'], ['j', 's', 'i'], ['h', 'p', 'q'], ['b', 'g', 'a'], ['m', 'e', 'n'], ['d', 'j', 'c'], ['j', 'i', 'c'], ['l', 'k', 'm'], ['b', 'a', 'c'], ['b', 'i', 'c'], ['e', 'n', 'f'], ['r', 'h', 'i'], ['g', 'p', 'o'], ['k', 's', 'j'], ['o', 'g', 'f'], ['b', 'g', 'h'], ['a', 'e', 'f'], ['m', 'n', 'q'], ['b', 'i', 'h'], ['l', 'm', 'e'], ['g', 'h', 'p'], ['k', 'r', 'm'], ['r', 'm', 'q'], ['r', 'h', 'q'], ['g', 'a', 'f']]
Coordinate Data:
d : [-156366809 / 10000000000, -2955891887 / 10000000000, 8423070439 / 10000000000]
c : [3212026749 / 10000000000, -6703101141 / 10000000000, -214773483 / 10000000000]
n : [2701391317 / 2500000000, 1268043563 / 1250000000, 15528269017 / 10000000000]
s : [-3650001951 / 5000000000, 1348382351 / 2000000000, -3071661061 / 10000000000]
q : [1180887713 / 1250000000, 2535655087 / 2000000000, 1487623281 / 2500000000]
p : [17333760687 / 10000000000, 13765695879 / 10000000000, -50399107 / 5000000000]
i : [802507677 / 5000000000, 2331447533 / 10000000000, -4188996003 / 10000000000]
m : [425658199 / 2500000000, 1190659579 / 1250000000, 1429397611 / 1250000000]
a : [2393775481 / 2500000000, -2401545843 / 10000000000, 6188967323 / 10000000000]
b : [10900351087 / 10000000000, -329571061 / 2500000000, -366345669 / 1000000000]
e : [3108573393 / 5000000000, 1284553353 / 10000000000, 14857116491 / 10000000000]
r : [187245487 / 2500000000, 655716729 / 625000000, 190969771 / 1250000000]
j : [-2945448909 / 5000000000, -647095491 / 2500000000, 1493337 / 62500000]
k : [-5877817471 / 10000000000, 2529409227 / 5000000000, 3341273699 / 5000000000]
l : [-113709327 / 312500000, 2458525591 / 10000000000, 8037677193 / 5000000000]
h : [936763397 / 1000000000, 1710119319 / 2000000000, -31575227 / 100000000]
f : [7950564029 / 5000000000, 83661509 / 400000000, 781073979 / 625000000]
g : [16202395427 / 10000000000, 2121759169 / 5000000000, 2736127501 / 10000000000]
o : [4672645619 / 2500000000, 1400628341 / 1250000000, 1894019117 / 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 = 8584416366278087125787570030095769519837476452863987374849 / 15337882503452577958364814181554127867500000000000000000000
Collision distance in [18703061 / 25000000, 14962449 / 20000000] ~ [0.74812, 0.74812]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2721 / 5000, 1361 / 2500] ~ [0.5442, 0.5444]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 15748011461438081337989 / 10000000000000000000000000000000000000000
rho in [125491081 / 100000000000000000, 1125491081 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [7403841 / 2856571372, 1852321 / 714142842] ~ [0.00259, 0.00259]
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, 20119 / 100000000] ~ [-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, 20119 / 5713142736] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [74812244 / 435889895, 74812245 / 435889894] ~ [0.17163, 0.17163]
Success: LHS < CD / |V| ^ .5
Success: existence proven