show/hide visualization coordinates
a : (0.2811788181600001, -0.18343716084881945, -0.26829119274421637)
b : (-0.24517525038483354, -1.0330854037204884, -0.23586941159139158)
c : (-0.45398362561097605, -0.3416418717023735, -0.9274650130157114)
d : (0.07109064717585784, 0.5088404693966607, -0.9586643244692754)
e : (0.8049723841509974, 0.667881959167895, -0.29826994122082545)
f : (1.0137800990535388, -0.02356205477338258, 0.3933253806638112)
g : (0.4887067781230964, -0.8740449755541504, 0.42452490304671253)
h : (-0.4624941666739778, -0.7076291107642678, 0.6843754902111823)
i : (-1.0067573426994687, -0.4002472739992351, -0.09619614917632174)
j : (-1.0723299220268556, -1.1157388659117153, -0.7917329754062852)
k : (-0.8241605799464846, 0.4899847742853206, -0.5135019769642937)
l : (-0.5345389832934861, 1.3022332620877957, -1.0198336267750219)
m : (-0.09730226864489944, 1.0728332033581855, -0.15023620477557287)
n : (0.44695998008896, 0.7654511869620481, 0.630335534400746)
o : (1.4242137909514763, 0.8861744140699054, 0.4559770235556504)
p : (0.2643640301774193, -0.12478135706240662, 1.0476415554196354)
q : (0.1826549833954173, -1.072669410381358, 1.3555894292289339)
r : (-0.28117937199577947, 0.1834382153903873, 0.2682914996122424)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['n', 'r', 'p'], ['j', 'i', 'c'], ['a', 'd', 'c'], ['f', 'n', 'p'], ['f', 'o', 'e'], ['l', 'm', 'k'], ['n', 'm', 'e'], ['i', 'k', 'c'], ['a', 'g', 'b'], ['h', 'p', 'q'], ['d', 'l', 'k'], ['h', 'r', 'i'], ['j', 'b', 'i'], ['f', 'g', 'p'], ['g', 'p', 'q'], ['a', 'e', 'f'], ['a', 'g', 'f'], ['r', 'k', 'm'], ['j', 'b', 'c'], ['g', 'h', 'q'], ['g', 'b', 'h'], ['a', 'd', 'e'], ['n', 'o', 'e'], ['d', 'k', 'c'], ['r', 'k', 'i'], ['a', 'b', 'c'], ['b', 'h', 'i'], ['n', 'r', 'm'], ['f', 'n', 'o'], ['d', 'm', 'e'], ['h', 'r', 'p'], ['d', 'l', 'm']]
Coordinate Data:
h : [-5291096618162914737 / 100000000000000000000, -4606377074596104817 / 25000000000000000000, 7867691858784414507 / 6250000000000000000]
e : [121455558464334598117 / 100000000000000000000, 29781399673707964781 / 25000000000000000000, 27618526597349861399 / 100000000000000000000]
f : [71168164977294366053 / 50000000000000000000, 780956207823501687 / 1562500000000000000, 3871122351432541 / 4000000000000000]
a : [34538100932617439839 / 50000000000000000000, 16996843346580209587 / 50000000000000000000, 30616401445010770813 / 100000000000000000000]
o : [183379699144382473879 / 100000000000000000000, 140954844185032911991 / 100000000000000000000, 51521611537498719263 / 50000000000000000000]
n : [85654318058130866943 / 100000000000000000000, 128882521474247161987 / 100000000000000000000, 24095814831901400789 / 20000000000000000000]
l : [-12495578280113745307 / 100000000000000000000, 182560728986821944321 / 100000000000000000000, -1781513678322790821 / 4000000000000000000]
m : [31228093184744919021 / 100000000000000000000, 31924144622772185267 / 20000000000000000000, 2121095012093756077 / 5000000000000000000]
r : [1605047856207114559 / 12500000000000000000, 17670306079270272523 / 25000000000000000000, 84274670680656649957 / 100000000000000000000]
d : [48067384766820649323 / 100000000000000000000, 103221449717708446151 / 100000000000000000000, -3842091172749513539 / 10000000000000000000]
k : [-8291547589082719113 / 20000000000000000000, 50667940103287216307 / 50000000000000000000, 6095323023003036257 / 100000000000000000000]
g : [89828997861544504609 / 100000000000000000000, -17533547388686340807 / 50000000000000000000, 24974502756025914237 / 25000000000000000000]
q : [29611909194388299329 / 50000000000000000000, -5492953826009343751 / 10000000000000000000, 96502231821162903469 / 50000000000000000000]
p : [1684868076674419741 / 2500000000000000000, 39859267071801700823 / 100000000000000000000, 162209676261395962031 / 100000000000000000000]
c : [-4440042511862739979 / 100000000000000000000, 18173215607805017781 / 100000000000000000000, -17650490291069365803 / 50000000000000000000]
j : [-258885438099416833 / 390625000000000000, -29618241906564586181 / 50000000000000000000, -21727776821196116097 / 100000000000000000000]
b : [1027549688171969433 / 6250000000000000000, -6371392199250811043 / 12500000000000000000, 16929289780146626013 / 50000000000000000000]
i : [-59717414220712000471 / 100000000000000000000, 769542211132428453 / 6250000000000000000, 23912952900900117967 / 50000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 41666602555733239752157016058734819930762834324044155081060177378191022983265728045364619440103655102860541456999230587 / 83333333260437894795919709176641128181887595686463977612801755281350188236516695000000000000000000000000000000000000000
Collision distance in [70710623 / 100000000, 2209707 / 3125000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [33 / 5000, 17 / 2500] ~ [0.0066, 0.0068]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 658723686925934707934857832607662343629692023467818221434645397303873 / 5000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [11478011 / 1000000000000, 11488011 / 1000000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [121 / 307920144, 289 / 692820323] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)