show/hide visualization coordinates
a : (0.3335159287699999, -0.689649367635, 0.626781716105)
b : (0.51491349907, -0.7145819357349998, -0.35631193939499994)
c : (1.27549121357, -0.7240428822349999, 0.292865466005)
d : (1.0665107642699998, -0.2582707700349999, 1.152739386805)
e : (0.13249074316999987, 0.09342412736500005, 1.215326487405)
f : (-0.5686649493300001, -0.2594098212349999, 0.595738876205)
g : (-0.36360491413000007, -1.0346630502349998, -0.0016996446950000021)
h : (-0.3344174173300001, -0.28429439843499993, -0.662077070995)
i : (0.5328315736699999, -0.0445672635349999, -1.098441120195)
j : (1.1484873314699997, 0.05810798156500008, -0.317143090895)
k : (1.70930193417, 0.15150770716500006, 0.505513473905)
l : (0.7537738023699999, 0.4462326594650001, 0.515659761205)
m : (-0.2200478345300001, 0.670513626465, 0.478655410905)
n : (-1.15587754413, 0.44913600096500006, 0.204402524205)
o : (-1.17955541253, -0.4799784242349999, -0.16463103969499998)
p : (-1.1342468171300002, 0.30328332456500007, -0.7846673709950001)
q : (-0.2573202387300001, 0.5614548815650001, -1.190061169195)
r : (0.3091549846699999, 0.5994484556650002, -0.366858764695)
s : (-0.5905190369300001, 1.035929391165, -0.375289784995)
t : (-1.97221761043, 0.1204197573650001, -0.270502106995)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['n', 't', 'p'], ['h', 'i', 'b'], ['r', 'i', 'j'], ['t', 'p', 'o'], ['q', 's', 'p'], ['m', 'r', 's'], ['c', 'j', 'k'], ['c', 'j', 'b'], ['n', 'f', 'o'], ['m', 'f', 'n'], ['f', 'e', 'a'], ['o', 'h', 'g'], ['l', 'j', 'k'], ['n', 't', 'o'], ['e', 'd', 'a'], ['h', 'q', 'p'], ['c', 'b', 'a'], ['h', 'q', 'i'], ['q', 'r', 's'], ['l', 'm', 'e'], ['l', 'd', 'k'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['l', 'r', 'j'], ['m', 's', 'n'], ['h', 'p', 'o'], ['l', 'm', 'r'], ['q', 'r', 'i'], ['g', 'f', 'a'], ['c', 'd', 'k'], ['m', 'f', 'e'], ['h', 'g', 'b'], ['l', 'e', 'd'], ['g', 'f', 'o'], ['i', 'j', 'b'], ['n', 's', 'p']]
Coordinate Data:
k : [5338937801 / 2500000000, 5828875251 / 10000000000, 4685187699 / 5000000000]
t : [-7729722121 / 5000000000, 5517995753 / 10000000000, 1610219589 / 10000000000]
e : [2793819647 / 5000000000, 5248039453 / 10000000000, 16468505533 / 10000000000]
s : [-1642458507 / 10000000000, 14673092091 / 10000000000, 562342809 / 10000000000]
g : [626682721 / 10000000000, -6032832323 / 10000000000, 1074561053 / 2500000000]
q : [67581179 / 400000000, 1985669399 / 2000000000, -7585371033 / 10000000000]
h : [918557689 / 10000000000, 294170839 / 2000000000, -2305530051 / 10000000000]
c : [8508821999 / 5000000000, -2926630643 / 10000000000, 7243895319 / 10000000000]
l : [5900234943 / 5000000000, 4388062387 / 5000000000, 9471838271 / 10000000000]
p : [-7079736309 / 10000000000, 293865257 / 400000000, -3531433051 / 10000000000]
j : [15747605177 / 10000000000, 978975599 / 2000000000, 4575239 / 40000000]
i : [9591047599 / 10000000000, 483515693 / 1250000000, -6669170543 / 10000000000]
a : [151957823 / 200000000, -2582695497 / 10000000000, 529152891 / 500000000]
b : [9411866853 / 10000000000, -1416010589 / 5000000000, 150424253 / 2000000000]
f : [-1423917631 / 10000000000, 1719699967 / 10000000000, 10272629421 / 10000000000]
m : [2062253517 / 10000000000, 2754733611 / 2500000000, 568862173 / 625000000]
d : [2985567901 / 2000000000, 1731090479 / 10000000000, 15842634527 / 10000000000]
o : [-7532822263 / 10000000000, -485986063 / 10000000000, 1334465131 / 5000000000]
r : [7354281709 / 10000000000, 644267671 / 625000000, 161663253 / 2500000000]
n : [-7296043579 / 10000000000, 8805158189 / 10000000000, 6359265901 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 31249953424105762177594389851819953685076250329154871640489 / 62500010530704882315790985507998393600225000000000000000000
Collision distance in [70710619 / 100000000, 3535531 / 5000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [347 / 1250, 1389 / 5000] ~ [0.2776, 0.2778]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1251216877329887364347465121761 / 10000000000000000000000000000000000000000
rho in [55928903 / 5000000000000, 55978903 / 5000000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [481636 / 734846923, 214369 / 326598632] ~ [0.00066, 0.00066]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [217729 / 100000000, 64529 / 25000000] ~ [0.00218, 0.00258]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [217729 / 5878775384, 64529 / 1469693844] ~ [4e-05, 4e-05]
CD / |V| ^ .5 in [70710619 / 447213596, 14142124 / 89442719] ~ [0.15811, 0.15811]
Success: LHS < CD / |V| ^ .5
Success: existence proven