show/hide visualization coordinates
a : (0.1762102921166666, 0.9063659585388889, -0.5367120589833332)
b : (-0.6188123057833333, 1.4962994806388887, -0.39558265698333317)
c : (0.19913429341666666, 1.6164584844388887, 0.16702304371666687)
d : (0.6114558238166665, 0.7229162295388888, 0.34471151911666686)
e : (0.9584345433166666, 0.2855252344388888, -0.48492387398333314)
f : (0.049538518516666685, -0.07215798136111118, -0.6993317402833331)
g : (-0.7461038812833334, 0.5234863133388888, -0.5890546091833332)
h : (-0.3832243294833334, 0.8138837589388889, 0.2963762205166669)
i : (0.02544977371666668, 0.05717950073888878, 0.806654716116667)
j : (0.8673384656166667, -0.24369100606111116, 0.3586587689166668)
k : (0.8071320596166667, -0.7020196470611112, -0.5280824815833332)
l : (-0.13242529198333336, -0.9864749808611112, -0.3375119011833332)
m : (-0.8727479732833334, -0.4553758289611112, -0.7496478231833331)
n : (-0.7349979697833333, -0.11500127156111117, 0.18049737891666684)
o : (-0.28670285628333336, -0.8789368842611112, 0.6446459227166669)
p : (0.5421103763166666, -0.7137025654611112, 1.1792170081166669)
q : (0.5973721425166667, -1.2053391732611112, 0.3101717947166669)
r : (-1.0591616810833333, -1.0494156217611113, 0.03289077251666683)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['n', 'i', 'o'], ['p', 'i', 'o'], ['e', 'a', 'f'], ['a', 'f', 'g'], ['c', 'd', 'h'], ['h', 'i', 'd'], ['l', 'q', 'o'], ['q', 'p', 'o'], ['c', 'a', 'd'], ['q', 'k', 'l'], ['n', 'm', 'g'], ['q', 'p', 'j'], ['h', 'n', 'i'], ['l', 'm', 'r'], ['h', 'c', 'b'], ['e', 'k', 'f'], ['e', 'a', 'd'], ['q', 'k', 'j'], ['h', 'n', 'g'], ['j', 'i', 'd'], ['l', 'm', 'f'], ['h', 'g', 'b'], ['m', 'f', 'g'], ['l', 'k', 'f'], ['e', 'j', 'd'], ['e', 'k', 'j'], ['n', 'r', 'o'], ['l', 'r', 'o'], ['a', 'g', 'b'], ['c', 'a', 'b'], ['p', 'j', 'i'], ['n', 'r', 'm']]
Coordinate Data:
l : [3848053113 / 10000000000, -1044136457 / 2500000000, 207398597 / 1000000000]
k : [13243626629 / 10000000000, -133199249 / 1000000000, 84140083 / 5000000000]
i : [542680377 / 1000000000, 1564999747 / 2500000000, 13515652143 / 10000000000]
c : [7163648967 / 10000000000, 874111553 / 400000000, 7119335419 / 10000000000]
n : [-435534733 / 2000000000, 907638253 / 2000000000, 7254078771 / 10000000000]
a : [3467204477 / 5000000000, 7375931783 / 5000000000, 10248049 / 1250000000]
f : [2833845609 / 5000000000, 4966624167 / 10000000000, -1544212421 / 10000000000]
r : [-2709655389 / 5000000000, -4805952237 / 10000000000, 5778012707 / 10000000000]
d : [11286864271 / 10000000000, 3229341569 / 2500000000, 8896220173 / 10000000000]
e : [7378325733 / 5000000000, 341738253 / 400000000, 299933121 / 5000000000]
b : [-40632681 / 400000000, 20651198787 / 10000000000, 373319603 / 2500000000]
q : [5573013729 / 5000000000, -795648469 / 1250000000, 8550822929 / 10000000000]
o : [230527747 / 1000000000, -1550582431 / 5000000000, 11895564209 / 10000000000]
m : [-35551737 / 100000000, 1134445691 / 10000000000, -8189493 / 40000000]
j : [13845690689 / 10000000000, 20320587 / 62500000, 9035692671 / 10000000000]
g : [-114436639 / 500000000, 5461533557 / 5000000000, -44144111 / 1000000000]
p : [2648352449 / 2500000000, -724410837 / 5000000000, 17241275063 / 10000000000]
h : [670031369 / 5000000000, 1382704157 / 1000000000, 8412867187 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 8061256562803397385042942431027612836319883868825133641 / 15999032025088513848660018141544049980121600000000000000
Collision distance in [70983027 / 100000000, 17745757 / 25000000] ~ [0.70983, 0.70983]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [306 / 625, 2449 / 5000] ~ [0.4896, 0.4898]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 575589200261466357983 / 500000000000000000000000000000000000000
rho in [53646491 / 50000000000000000, 553646491 / 50000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [13872 / 6415003, 5997601 / 2771281292] ~ [0.00216, 0.00216]
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, 10063 / 50000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [692820323 / 12500000, 173205081 / 3125000] ~ [55.42563, 55.42563]
LHS := (LHS NUM) / (LHS DEN) in [-4997 / 1385640646, 10063 / 2771281292] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70983027 / 424264069, 17745757 / 106066017] ~ [0.16731, 0.16731]
Success: LHS < CD / |V| ^ .5
Success: existence proven