show/hide visualization coordinates
a : (-0.12703865950000004, -0.8583881687631578, 0.2587431649842105)
b : (-0.5041131885, -0.7528221125631579, -0.6614038930157895)
c : (0.4245305358, -1.102926820263158, -0.5387355309157895)
d : (0.7132204888, -0.35456272516315784, 0.0584321917842105)
e : (0.22118100509999994, -0.18673677736315786, 0.9126754806842106)
f : (-0.6754639111, -0.6056988429631579, 1.0558490856842107)
g : (-1.0546955932, -0.5057153061631579, 0.1359650579842105)
h : (-0.6330602254000001, 0.20939053793684215, -0.4215717096157895)
i : (-0.42693157410000004, -0.04726238776315783, -1.3658387547157895)
j : (0.08289506989999995, -0.9026968116631578, -1.4569910229157894)
k : (0.44207688589999994, -0.16505235706315785, -0.8852663654157895)
l : (0.7662967218000001, 0.5777005224368421, -0.29943391291578947)
m : (0.9928818681, 0.39577550933684225, 0.6574163692842105)
n : (0.14005825169999997, 0.8078093438368421, 0.9782278385842105)
o : (-0.4236160511, 0.22078848253684213, 1.5593283379842107)
p : (-0.5998158476000001, 0.2684554565368421, 0.5761287191842106)
q : (-0.11008270670000003, 0.9390678908368422, 0.018956920184210524)
r : (0.02650476469999996, 0.7420649414368421, -0.9518848281157894)
s : (0.7451721653999999, 1.3208096248368422, 0.3694028512842105)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['e', 'a', 'd'], ['k', 'c', 'j'], ['m', 'n', 's'], ['e', 'a', 'f'], ['q', 'h', 'p'], ['e', 'm', 'n'], ['g', 'h', 'p'], ['i', 'j', 'b'], ['l', 'm', 's'], ['n', 'o', 'p'], ['i', 'h', 'b'], ['a', 'c', 'b'], ['g', 'a', 'b'], ['g', 'f', 'p'], ['g', 'h', 'b'], ['r', 'h', 'i'], ['q', 'n', 's'], ['e', 'f', 'o'], ['k', 'c', 'd'], ['l', 'q', 's'], ['g', 'a', 'f'], ['l', 'r', 'q'], ['c', 'j', 'b'], ['l', 'k', 'd'], ['m', 'e', 'd'], ['a', 'c', 'd'], ['l', 'r', 'k'], ['q', 'r', 'h'], ['r', 'i', 'k'], ['f', 'o', 'p'], ['i', 'k', 'j'], ['e', 'n', 'o'], ['q', 'n', 'p'], ['l', 'm', 'd']]
Coordinate Data:
r : [5316782013 / 10000000000, 7034767633 / 5000000000, -1383146979 / 2500000000]
s : [625172801 / 500000000, 198569821 / 100000000, 3840144439 / 5000000000]
h : [-79929243 / 625000000, 8742791231 / 10000000000, -229456731 / 10000000000]
p : [-94642411 / 1000000000, 9333440417 / 10000000000, 9747547557 / 10000000000]
n : [6452316883 / 10000000000, 1472697929 / 1000000000, 13768538751 / 10000000000]
f : [-340580949 / 2000000000, 295948711 / 5000000000, 7272375611 / 5000000000]
g : [-2747610783 / 5000000000, 159173279 / 1000000000, 1069182189 / 2000000000]
q : [3950907299 / 10000000000, 400989119 / 250000000, 4175829567 / 10000000000]
j : [1176137013 / 2000000000, -475616453 / 2000000000, -1322956233 / 1250000000]
i : [6259349 / 80000000, 3088130987 / 5000000000, -4836063591 / 5000000000]
m : [14980553047 / 10000000000, 2121328189 / 2000000000, 5280212029 / 5000000000]
e : [7263544417 / 10000000000, 2390759039 / 5000000000, 3278253793 / 2500000000]
l : [794668849 / 625000000, 3106472769 / 2500000000, 247980309 / 2500000000]
k : [378900129 / 400000000, 4998362281 / 10000000000, -4866403289 / 10000000000]
o : [163114771 / 2000000000, 8856770677 / 10000000000, 3915908749 / 2000000000]
d : [6091969627 / 5000000000, 15516293 / 50000000, 4570582283 / 10000000000]
b : [10602481 / 10000000000, -439667637 / 5000000000, -525555713 / 2000000000]
c : [2324259931 / 2500000000, -4380382351 / 10000000000, -43784217 / 312500000]
a : [3781347771 / 10000000000, -483748959 / 2500000000, 1314738403 / 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 = 1662057722514387459509082317305994619627757114074487202907 / 3333308115451010555289835560993700436140000000000000000000
Collision distance in [70613107 / 100000000, 17653277 / 25000000] ~ [0.70613, 0.70613]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1061 / 2000, 5307 / 10000] ~ [0.5305, 0.5307]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 267818340855607172624669 / 2000000000000000000000000000000000000000
rho in [115719129 / 10000000000000000, 215719129 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [28143025 / 11426285488, 9388083 / 3808761824] ~ [0.00246, 0.00246]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-4969 / 25000000, 20233 / 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 [-4969 / 1428285684, 20233 / 5713142736] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70613107 / 435889895, 35306554 / 217944947] ~ [0.162, 0.162]
Success: LHS < CD / |V| ^ .5
Success: existence proven