show/hide visualization coordinates
a : (-0.07617699261499994, 0.7652367024650001, 0.7883037504400001)
b : (-0.5508636036149999, -0.08758632333499994, 1.00593993294)
c : (0.42387217738500005, -0.10074386543499991, 0.7829667591400001)
d : (0.732232453385, 0.6582292069650001, 0.20949155014000015)
e : (-0.16055236771499998, 0.8326715981650001, -0.20584580105999983)
f : (-0.946091716515, 0.549914232365, 0.34458694094000014)
g : (-0.925329489815, 0.7862659510650001, 1.3160326650400003)
h : (-0.8991508562149999, -0.42605435333499997, 0.13179155754000016)
i : (-0.144802156415, -0.8995097022349999, 0.5865421173400002)
j : (0.844812130285, -1.002700869835, 0.6866178200400002)
k : (1.1738588512850001, -0.23591127233499987, 0.13547177014000017)
l : (1.4934037073850002, 0.5275726161650001, -0.4257620821599999)
m : (0.6758182942850001, 1.022462197365, -0.7201060893599998)
n : (-0.06987219511499992, 0.512420130665, -1.1488283585599999)
o : (-0.866959785715, 0.2485928614650001, -0.6056464876599998)
p : (-1.160806477315, -0.6878735073349999, -0.7971794142599999)
q : (-0.46874633971499996, -1.215943356235, -0.3050463016599999)
r : (0.44887804408500004, -0.828818340835, -0.21504789695999982)
s : (0.671311361285, 0.022943401965000054, -0.6894162694599999)
t : (-0.194835038615, -0.4411673077349999, -0.8748661625599998)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['o', 'e', 'n'], ['f', 'g', 'b'], ['o', 'h', 'p'], ['k', 'j', 'c'], ['o', 't', 'p'], ['t', 'q', 'r'], ['f', 'h', 'b'], ['d', 'm', 'l'], ['d', 'c', 'a'], ['p', 'h', 'q'], ['h', 'q', 'i'], ['m', 'l', 's'], ['b', 'a', 'g'], ['d', 'e', 'a'], ['m', 'e', 'n'], ['t', 'r', 's'], ['f', 'a', 'g'], ['f', 'e', 'a'], ['r', 'k', 'j'], ['t', 's', 'n'], ['m', 's', 'n'], ['d', 'k', 'c'], ['c', 'a', 'b'], ['k', 'r', 's'], ['i', 'c', 'b'], ['o', 't', 'n'], ['d', 'm', 'e'], ['r', 'j', 'i'], ['p', 't', 'q'], ['q', 'r', 'i'], ['f', 'o', 'e'], ['d', 'l', 'k'], ['k', 'l', 's'], ['i', 'h', 'b'], ['j', 'c', 'i'], ['f', 'o', 'h']]
Coordinate Data:
d : [-564234573 / 2000000000, -220505671 / 1250000000, 2104602689 / 5000000000]
s : [-276495243 / 1250000000, 2294406341 / 5000000000, 6599141787 / 5000000000]
k : [-1809359211 / 2500000000, 287094377 / 400000000, 2474701589 / 5000000000]
r : [3092807 / 2500000000, 1310643011 / 1000000000, 8454599849 / 10000000000]
n : [259993681 / 500000000, -61190921 / 2000000000, 3558480893 / 2000000000]
j : [-1973484817 / 5000000000, 74226277 / 50000000, -562057321 / 10000000000]
a : [1052584319 / 2000000000, -2834120323 / 10000000000, -12631333 / 80000000]
o : [6585374763 / 5000000000, 2332318087 / 10000000000, 3090146439 / 2500000000]
m : [-1128515637 / 5000000000, -675796909 / 1250000000, 13505181773 / 10000000000]
b : [2001957541 / 2000000000, 1138821987 / 2000000000, -75105569 / 200000000]
q : [4594307533 / 5000000000, 2122210033 / 1250000000, 1169322987 / 1250000000]
l : [-2086577081 / 2000000000, -22873973 / 500000000, 10561741701 / 10000000000]
f : [6981034417 / 5000000000, -340447811 / 5000000000, 285825147 / 1000000000]
p : [8054608221 / 5000000000, 467879271 / 400000000, 7137957511 / 5000000000]
i : [5949173233 / 10000000000, 3453335931 / 2500000000, 219349853 / 5000000000]
g : [13754446567 / 10000000000, -3044412809 / 10000000000, -6856205771 / 10000000000]
e : [3053337673 / 5000000000, -21927933 / 62500000, 836257889 / 1000000000]
t : [1289900411 / 2000000000, 9229919779 / 10000000000, 3010556501 / 2000000000]
h : [13492660231 / 10000000000, 1815758047 / 2000000000, 623275663 / 1250000000]
c : [52485979 / 2000000000, 1456421339 / 2500000000, -190693339 / 1250000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 124999999974411048985945891486102516966556413108246906758361 / 249999999980921132919078117374334814881150000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5311 / 10000, 5313 / 10000] ~ [0.5311, 0.5313]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1531407195764794168853 / 1250000000000000000000000000000000000000
rho in [110685399 / 100000000000000000, 1110685399 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [28206721 / 11757550768, 3136441 / 1306394528] ~ [0.0024, 0.0024]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-4997 / 25000000, 20123 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-4997 / 1469693844, 20123 / 5878775376] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [35355339 / 223606798, 70710679 / 447213595] ~ [0.15811, 0.15811]
Success: LHS < CD / |V| ^ .5
Success: existence proven