show/hide visualization coordinates
a : (-0.48386895849411765, -0.20099282477647062, -0.9705117808588235)
b : (0.2910639334058824, 0.28141586782352934, -0.5621481360588235)
c : (0.15070658640588236, -0.6903089747764706, -0.37227806155882354)
d : (-0.6670041546941177, -0.2606268780764706, 0.01076559044117642)
e : (-0.48609536369411765, 0.6278385582235293, -0.4110177400588235)
f : (-0.17313347999411766, 0.6660311345235295, -1.3600152038588236)
g : (0.2305792037058823, 1.2731195369235293, -0.6755740153588236)
h : (0.5969159542058824, 0.8881688383235293, 0.17154483384117647)
i : (0.5644650554058823, -0.10008788687647063, 0.3208618930411765)
j : (0.5093418558058824, -1.0869486032764706, 0.4727413161411764)
k : (-0.45272910769411767, -1.2123678184764706, 0.2304821949411765)
l : (-0.18662500979411767, -0.4819009431764706, 0.8594549712411765)
m : (-0.23015312699411766, 0.4653459298235294, 0.5419196751411766)
n : (-0.26267142729411763, 1.3989761866235293, 0.1851605073411765)
o : (0.6011833556058823, 1.8779852919235294, 0.02925928474117645)
p : (-0.13580529469411762, -1.4368024460764706, 1.1519963808411764)
q : (0.13382997880588238, -2.0088449686764704, 0.3773582900411765)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['b', 'f', 'a'], ['n', 'g', 'o'], ['i', 'l', 'j'], ['k', 'q', 'j'], ['n', 'e', 'm'], ['g', 'f', 'e'], ['i', 'b', 'h'], ['d', 'l', 'm'], ['d', 'e', 'm'], ['b', 'g', 'f'], ['i', 'j', 'c'], ['d', 'k', 'l'], ['q', 'p', 'j'], ['n', 'h', 'm'], ['l', 'p', 'j'], ['i', 'b', 'c'], ['d', 'c', 'a'], ['i', 'l', 'm'], ['n', 'h', 'o'], ['n', 'g', 'e'], ['d', 'e', 'a'], ['d', 'k', 'c'], ['g', 'o', 'h'], ['b', 'g', 'h'], ['p', 'k', 'q'], ['k', 'l', 'p'], ['f', 'e', 'a'], ['c', 'b', 'a'], ['i', 'h', 'm'], ['k', 'j', 'c']]
Coordinate Data:
g : [3588253559 / 5000000000, 8499929029 / 5000000000, -336941001 / 5000000000]
q : [6209014869 / 10000000000, -7909893499 / 5000000000, 2463860263 / 2500000000]
e : [2440361 / 2500000000, 10547048271 / 10000000000, 1971680751 / 10000000000]
i : [2103073127 / 2000000000, 163389191 / 500000000, 4645238541 / 5000000000]
m : [2569183811 / 10000000000, 8922121987 / 10000000000, 11501054903 / 10000000000]
j : [9964133639 / 10000000000, -412551459 / 625000000, 10809271313 / 10000000000]
k : [85856001 / 2500000000, -981876937 / 1250000000, 8386680101 / 10000000000]
o : [10882548637 / 10000000000, 2881064451 / 1250000000, 6374450999 / 10000000000]
h : [10839874623 / 10000000000, 410948471 / 312500000, 779730649 / 1000000000]
c : [1275556189 / 2000000000, -2634427059 / 10000000000, 73721173 / 312500000]
p : [1756331067 / 5000000000, -2524840443 / 2500000000, 440045549 / 250000000]
n : [280500101 / 1250000000, 3651684911 / 2000000000, 317338529 / 400000000]
d : [-899663233 / 5000000000, 415598477 / 2500000000, 773689257 / 1250000000]
b : [1556270883 / 2000000000, 7082821367 / 10000000000, 460376791 / 10000000000]
a : [4003187 / 1250000000, 2258734441 / 10000000000, -3623259657 / 10000000000]
l : [3004464983 / 10000000000, -550346743 / 10000000000, 1834550983 / 1250000000]
f : [3139380281 / 10000000000, 5464487017 / 5000000000, -7518293887 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 140227366505378942973227946604318761337021145305061739645027 / 327991895637806871628188868720211669613800000000000000000000
Collision distance in [65386009 / 100000000, 6538601 / 10000000] ~ [0.65386, 0.65386]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1417 / 2500, 567 / 1000] ~ [0.5668, 0.567]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 9279747791440523212041 / 10000000000000000000000000000000000000000
rho in [38532579 / 40000000000000000, 438532579 / 40000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [2007889 / 670820394, 8037225 / 2683281572] ~ [0.00299, 0.003]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19991 / 100000000, 2513 / 12500000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-19991 / 5366563144, 2513 / 670820393] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [65386009 / 412310563, 32693005 / 206155281] ~ [0.15858, 0.15858]
Success: LHS < CD / |V| ^ .5
Success: existence proven