show/hide visualization coordinates
a : (-0.47541515905263154, 1.442265286494737, -1.2500103319842106)
b : (-0.3699552310526316, 0.44790857719473687, -1.2395285536842107)
c : (-1.0806317685526317, 0.8693962817947369, -1.8027861465842105)
d : (-0.8345558013526316, 1.786068786794737, -2.1176621556842106)
e : (-1.4446632272526316, 1.6738079425947368, -1.3333309013842105)
f : (-1.1658886263526318, 0.8708943756947369, -0.8064264823842107)
g : (-0.2602097854526316, 0.9712799414947368, -0.39450504258421054)
h : (0.26450382034736836, 0.13156352619473688, -0.5343012269842107)
i : (-0.7219414487526316, 0.0844526419947369, -0.37698015268421053)
j : (-0.10843671645263164, 0.3435245207947369, 0.36900960701578944)
k : (0.7479269587473684, -0.16658175970526307, 0.2887414667157895)
l : (-0.11707938255263162, -0.5982604103052631, 0.032906914515789476)
m : (0.08380370364736839, -0.41249369460526314, 0.9947385769157895)
n : (1.0614611539473684, -0.5401419843052631, 1.1617666157157895)
o : (0.5848577638473683, -1.1284103084052632, 0.5084821411157895)
p : (0.40545420244736835, -1.2207952795052632, 1.4878984908157895)
q : (1.2491209769473683, -1.0547303659052631, 1.9984276901157894)
r : (1.2840473467473683, -1.513719667605263, 1.1106814246157894)
s : (0.8976012201473684, -1.9860284107052633, 1.9028780664157894)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['e', 'a', 'f'], ['r', 'p', 's'], ['j', 'h', 'g'], ['l', 'm', 'o'], ['p', 'q', 'n'], ['a', 'c', 'b'], ['r', 'q', 'n'], ['a', 'c', 'd'], ['g', 'h', 'b'], ['l', 'i', 'j'], ['r', 'o', 'n'], ['j', 'i', 'g'], ['k', 'l', 'o'], ['e', 'c', 'd'], ['h', 'i', 'b'], ['r', 'p', 'o'], ['k', 'j', 'm'], ['p', 'q', 's'], ['p', 'm', 'n'], ['e', 'f', 'c'], ['l', 'j', 'm'], ['k', 'o', 'n'], ['f', 'i', 'g'], ['a', 'b', 'g'], ['o', 'p', 'm'], ['k', 'h', 'j'], ['e', 'a', 'd'], ['k', 'm', 'n'], ['f', 'i', 'b'], ['f', 'c', 'b'], ['k', 'h', 'l'], ['a', 'f', 'g'], ['l', 'h', 'i'], ['r', 's', 'q']]
Coordinate Data:
p : [616604963 / 5000000000, 17032197223 / 10000000000, -61951423 / 62500000]
o : [-70103211 / 1250000000, 2013543439 / 1250000000, -118064183 / 10000000000]
l : [403659111 / 625000000, 10806848531 / 10000000000, 4637688083 / 10000000000]
g : [1577969961 / 2000000000, -4888554987 / 10000000000, 4455903827 / 5000000000]
i : [6253583219 / 5000000000, 497464751 / 1250000000, 1747311751 / 2000000000]
j : [1274423823 / 2000000000, 69449961 / 500000000, 638330579 / 5000000000]
n : [-5326859589 / 10000000000, 10225664271 / 10000000000, -6650908929 / 10000000000]
q : [-7203457819 / 10000000000, 15371548087 / 10000000000, -15017519673 / 10000000000]
s : [-3688260251 / 10000000000, 4936905707 / 2000000000, -3515505859 / 2500000000]
d : [3408327491 / 2500000000, -162955543 / 125000000, 5228675757 / 2000000000]
h : [2642713747 / 10000000000, 1754304583 / 5000000000, 5154884749 / 5000000000]
r : [-7552721517 / 10000000000, 1247590069 / 625000000, -3070028509 / 5000000000]
e : [19734384223 / 10000000000, -5956917499 / 5000000000, 9150033121 / 5000000000]
k : [-2191517637 / 10000000000, 259602481 / 400000000, 2079342561 / 10000000000]
c : [4023517409 / 2500000000, -386971839 / 1000000000, 11497309347 / 5000000000]
m : [2224857457 / 5000000000, 4474590687 / 5000000000, -4980628541 / 10000000000]
f : [8473319107 / 5000000000, -3884699329 / 10000000000, 3257755513 / 2500000000]
b : [8987304261 / 10000000000, 337069 / 9765625, 3472408553 / 2000000000]
a : [10041903541 / 10000000000, -9598408437 / 10000000000, 4366715137 / 2500000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 11363390376238783423409869437740025461857086187122978074891 / 22728882652351689527227409887975938348600000000000000000000
Collision distance in [4419213 / 6250000, 70707409 / 100000000] ~ [0.70707, 0.70707]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [583 / 2000, 2917 / 10000] ~ [0.2915, 0.2917]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 154411740294065295086286307710243 / 5000000000000000000000000000000000000000
rho in [17573 / 100000000, 8787 / 50000000] ~ [0.00018, 0.00018]
sigma_min ^ 2 / (16 * E ^ .5) in [8497225 / 11426285488, 8508889 / 11426285472] ~ [0.00074, 0.00074]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [3653043 / 100000000, 462019 / 12500000] ~ [0.03653, 0.03696]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [3653043 / 5713142744, 462019 / 714142842] ~ [0.00064, 0.00065]
CD / |V| ^ .5 in [70707408 / 435889895, 70707409 / 435889894] ~ [0.16221, 0.16221]
Success: LHS < CD / |V| ^ .5
Success: existence proven