show/hide visualization coordinates
a : (0.54573474505, 0.910500927127778, 1.0219921665555556)
b : (0.15604716905000005, 0.8649412864277779, 0.10217266675555553)
c : (-0.43872917344999995, 1.026023330127778, 0.8897599175555556)
d : (-0.007154479149999948, 0.1464537623277779, 0.6895084290555554)
e : (0.98498925225, 0.04885744212777793, 0.7677757574555556)
f : (1.5314826420500003, 0.796292504727778, 1.1455134997555554)
g : (1.1484531798500002, 0.8726328534277779, 0.22493727675555553)
h : (0.7022091544500001, 0.08020095012777789, -0.1908967626444445)
i : (-0.15942284494999998, 0.2902299778277779, -0.6529336714444445)
j : (-0.7636220980499999, 0.47278466312777784, 0.12270609625555551)
k : (-0.49721317024999995, -0.4906654219722221, 0.09459530575555553)
l : (0.43820945055000005, -0.6948663680722221, 0.3831893009555555)
m : (0.14658152165000005, -0.6584087617722221, -0.5726475019444445)
n : (-0.43022783774999995, -0.3824714853722221, -1.3415100269444444)
o : (-1.07527497515, -0.1104740002722221, -0.6274151043444445)
p : (-0.7629592334499999, -1.0587483449722221, -0.6842890388444445)
q : (-0.13910354924999996, -1.4203720967722222, 0.00855462845555549)
r : (-1.37999975345, -0.6929112181722221, -1.3810129391444446)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['l', 'k', 'd'], ['n', 'i', 'o'], ['e', 'a', 'f'], ['a', 'f', 'g'], ['q', 'p', 'm'], ['e', 'h', 'l'], ['c', 'a', 'd'], ['h', 'm', 'i'], ['h', 'm', 'l'], ['n', 'p', 'm'], ['q', 'p', 'k'], ['q', 'k', 'l'], ['p', 'k', 'o'], ['h', 'i', 'b'], ['p', 'r', 'o'], ['e', 'a', 'd'], ['j', 'i', 'o'], ['c', 'j', 'd'], ['n', 'm', 'i'], ['h', 'g', 'b'], ['l', 'e', 'd'], ['l', 'q', 'm'], ['e', 'f', 'g'], ['e', 'g', 'h'], ['j', 'i', 'b'], ['c', 'j', 'b'], ['k', 'j', 'o'], ['n', 'r', 'p'], ['k', 'j', 'd'], ['n', 'r', 'o'], ['a', 'g', 'b'], ['c', 'a', 'b']]
Coordinate Data:
k : [73633363 / 10000000000, -350658507 / 10000000000, 4837328919 / 10000000000]
l : [9427859571 / 10000000000, -37385437 / 156250000, 7723268871 / 10000000000]
i : [431442077 / 1250000000, 7458295491 / 10000000000, -2637960853 / 10000000000]
c : [658473331 / 10000000000, 7408114507 / 5000000000, 12788975037 / 10000000000]
n : [23233959 / 312500000, 731280859 / 10000000000, -1190465551 / 1250000000]
a : [2625778129 / 2500000000, 1707625623 / 1250000000, 14111297527 / 10000000000]
f : [10180295743 / 5000000000, 312973019 / 250000000, 15346510859 / 10000000000]
r : [-8754232469 / 10000000000, -2373116469 / 10000000000, -991875353 / 1000000000]
d : [2487110137 / 5000000000, 752566667 / 1250000000, 1348307519 / 1250000000]
e : [3723914397 / 2500000000, 2522285067 / 5000000000, 2892283359 / 2500000000]
b : [1651559189 / 2500000000, 13205408577 / 10000000000, 4913102529 / 10000000000]
q : [3654729573 / 10000000000, -1929545051 / 2000000000, 1988461073 / 5000000000]
o : [-2853492343 / 5000000000, 345125571 / 1000000000, -1191387591 / 5000000000]
m : [3255790141 / 5000000000, -405618381 / 2000000000, -917549579 / 5000000000]
j : [-518091183 / 2000000000, 1160480293 / 1250000000, 639804603 / 1250000000]
g : [516571777 / 312500000, 13282324247 / 10000000000, 6140748629 / 10000000000]
p : [-2583827269 / 10000000000, -6031487737 / 10000000000, -2951514527 / 10000000000]
h : [1206785661 / 1000000000, 2679002607 / 5000000000, 396481647 / 2000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 468809645756515189769636722690784956122449888232751178383369 / 996854046362808018389900919529747598033700000000000000000000
Collision distance in [68577631 / 100000000, 2143051 / 3125000] ~ [0.68578, 0.68578]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [4533 / 10000, 907 / 2000] ~ [0.4533, 0.4535]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 5961513041953359590163 / 5000000000000000000000000000000000000000
rho in [10919261 / 10000000000000000, 110919261 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [2283121 / 1231680576, 20566225 / 11085125168] ~ [0.00185, 0.00186]
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, 2517 / 12500000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [692820323 / 12500000, 173205081 / 3125000] ~ [55.42563, 55.42563]
LHS := (LHS NUM) / (LHS DEN) in [-19987 / 5542562584, 2517 / 692820323] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [68577631 / 424264069, 17144408 / 106066017] ~ [0.16164, 0.16164]
Success: LHS < CD / |V| ^ .5
Success: existence proven