show/hide visualization coordinates
a : (-0.8204495252666666, -0.7954657533388889, 0.2582908457277777)
b : (-0.3273888791666666, -0.11020735573888896, 0.7943058898277777)
c : (-0.9693739401666666, 0.17785902346111104, 0.08376177262777768)
d : (-1.5212503983666665, -0.5058898503388889, -0.39364775007222236)
e : (-0.6619968895666666, -0.8965634809388889, -0.7238863336722223)
f : (0.10878030623333346, -0.925821503038889, -0.0874537114722223)
g : (-0.09042911466666659, -1.0778837629388889, 0.8806334103277778)
h : (0.6076944939333334, -0.4141889960388889, 0.6120581260277776)
i : (0.44045659513333346, 0.5094449644611111, 0.9569230158277777)
j : (-0.4060808004666665, 0.8572839816611111, 0.5539559503277777)
k : (-0.23256185856666656, 0.6426782701611111, -0.40720770127222233)
l : (-0.8773753031666665, 0.06295957516111106, -0.9053460918722225)
m : (0.07456372483333346, -0.2244203857388889, -0.7993987221722223)
n : (0.9366085149333334, -0.421081753538889, -0.3322765902722223)
o : (1.1445479914333334, 0.35432770846111106, 0.2639627411277777)
p : (0.47539438463333344, 1.087296691261111, 0.1415294100277777)
q : (0.7324082916333334, 0.5102824519611111, -0.6337114680722225)
r : (1.3864524066333335, 1.169390175061111, -0.26249279297222233)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['p', 'i', 'o'], ['e', 'a', 'f'], ['a', 'f', 'g'], ['e', 'm', 'f'], ['h', 'n', 'f'], ['q', 'p', 'r'], ['c', 'a', 'd'], ['q', 'p', 'k'], ['q', 'r', 'o'], ['h', 'i', 'b'], ['h', 'n', 'o'], ['h', 'f', 'g'], ['e', 'a', 'd'], ['p', 'r', 'o'], ['l', 'k', 'm'], ['q', 'n', 'o'], ['h', 'g', 'b'], ['l', 'e', 'd'], ['p', 'k', 'j'], ['h', 'i', 'o'], ['q', 'n', 'm'], ['c', 'd', 'l'], ['c', 'k', 'l'], ['j', 'i', 'b'], ['c', 'j', 'b'], ['n', 'm', 'f'], ['a', 'g', 'b'], ['e', 'm', 'l'], ['q', 'k', 'm'], ['c', 'k', 'j'], ['c', 'a', 'b'], ['p', 'j', 'i']]
Coordinate Data:
k : [7060465683 / 10000000000, -25679949 / 200000000, 1725472329 / 2000000000]
l : [13508600129 / 10000000000, 9026379 / 20000000, 13608745551 / 10000000000]
i : [165140573 / 5000000000, 48335607 / 10000000000, -2506972763 / 5000000000]
c : [14428586499 / 10000000000, 3364195017 / 10000000000, 1858833453 / 5000000000]
n : [-1157809513 / 2500000000, 9353602787 / 10000000000, 1575610107 / 2000000000]
a : [258786847 / 200000000, 2619488557 / 2000000000, 78895047 / 400000000]
f : [729408807 / 2000000000, 7200500141 / 5000000000, 5429821747 / 10000000000]
r : [-9129676969 / 10000000000, -6551116499 / 10000000000, 3590106281 / 5000000000]
d : [19947351081 / 10000000000, 2040336751 / 2000000000, 8491762133 / 10000000000]
e : [11354815993 / 10000000000, 14108420061 / 10000000000, 11794147969 / 10000000000]
b : [8008735889 / 10000000000, 6244858809 / 10000000000, -1693887133 / 5000000000]
q : [-2589235819 / 10000000000, 9990183 / 2500000000, 10892399313 / 10000000000]
o : [-6710632817 / 10000000000, 1599508167 / 10000000000, 1915657221 / 10000000000]
m : [3989209849 / 10000000000, 7386989109 / 10000000000, 6274635927 / 5000000000]
j : [4397827551 / 5000000000, -686010913 / 2000000000, -984274871 / 10000000000]
g : [1409784561 / 2500000000, 15921622881 / 10000000000, -4251049471 / 10000000000]
p : [-19096749 / 10000000000, -5730181661 / 10000000000, 784997633 / 2500000000]
h : [-671048921 / 5000000000, 2321168803 / 2500000000, -391324157 / 2500000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 488281249855810879566024404256738342666497488805310064609 / 976562500082203937853454374054882795614453125000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [6109 / 10000, 6111 / 10000] ~ [0.6109, 0.6111]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1685813155707321604543 / 1250000000000000000000000000000000000000
rho in [116131413 / 100000000000000000, 1116131413 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [37319881 / 11085125184, 37344321 / 11085125168] ~ [0.00337, 0.00337]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-1999 / 10000000, 10051 / 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 [-9995 / 2771281292, 10051 / 2771281292] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710678 / 424264069, 70710679 / 424264068] ~ [0.16667, 0.16667]
Success: LHS < CD / |V| ^ .5
Success: existence proven