show/hide visualization coordinates
a : (-0.11930959914099504, 0.5174775875938004, -0.1606006222903567)
b : (0.4293523249749203, 1.01202391359185, 0.5134880994934345)
c : (0.8513496165340921, 0.6857629292082865, -0.3323672848674069)
d : (0.3031672155097806, 0.18942043895793725, -1.0055218387652505)
e : (-0.6670089848525562, 0.019337315290827273, -0.832823807893885)
f : (-1.089005616406126, 0.34559927174832106, 0.013031951075931636)
g : (-0.5408253631235547, 0.8419412541444412, 0.6861865903697189)
h : (0.1540545919445912, 0.35909567324352887, 1.2191049553359379)
i : (0.5777226220599484, 0.03297453772640091, 0.374029909168533)
j : (0.9980479655258777, -0.293425072644114, -0.47260580505127253)
k : (1.2733468286061829, 0.35950383397160324, -1.1782221164398867)
l : (0.027885288848035428, -0.4648838388554559, -0.30117307488427153)
m : (-0.9423088549140912, -0.6335904523502132, -0.12720680271474621)
n : (-1.6371888823846235, -0.15074476549052562, -0.6601236657678067)
o : (-0.39535261827256885, -0.137611823607523, 0.5472165174148718)
p : (0.3007525064033359, -0.6200916580076934, 1.0788657118370415)
q : (0.7227487653649037, -0.9463530651075434, 0.2330112034153818)
r : (-0.24742780667715225, -1.1164360794139283, 0.4057100805640308)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['b', 'c', 'i'], ['j', 'i', 'c'], ['a', 'd', 'c'], ['g', 'h', 'o'], ['l', 'm', 'e'], ['n', 'm', 'e'], ['d', 'l', 'e'], ['a', 'g', 'b'], ['j', 'l', 'q'], ['d', 'l', 'j'], ['l', 'r', 'm'], ['a', 'e', 'f'], ['a', 'g', 'f'], ['f', 'm', 'n'], ['n', 'e', 'f'], ['d', 'k', 'j'], ['l', 'r', 'q'], ['r', 'p', 'q'], ['r', 'o', 'p'], ['j', 'i', 'q'], ['g', 'b', 'h'], ['h', 'p', 'i'], ['j', 'k', 'c'], ['a', 'd', 'e'], ['f', 'g', 'o'], ['p', 'i', 'q'], ['h', 'o', 'p'], ['d', 'k', 'c'], ['a', 'b', 'c'], ['b', 'h', 'i'], ['f', 'm', 'o'], ['r', 'm', 'o']]
Coordinate Data:
h : [20260519406546454011 / 50000000000000000000, 7857364496148600129 / 25000000000000000000, -84007256518425482181 / 100000000000000000000]
e : [24525479298561530061 / 20000000000000000000, 16351323444966140529 / 25000000000000000000, 60592809902278410077 / 50000000000000000000]
f : [82413529824082307353 / 50000000000000000000, 1638954906705759141 / 5000000000000000000, 4575005488446893989 / 12500000000000000000]
a : [67857457921651533093 / 100000000000000000000, 15591266549567248737 / 100000000000000000000, 43170640995363189 / 80000000000000000]
o : [95461759834808910917 / 100000000000000000000, 20275051917424895473 / 25000000000000000000, -8409206363159431419 / 50000000000000000000]
l : [53137969122748479889 / 100000000000000000000, 113827409194492873629 / 100000000000000000000, 34010273251797734731 / 50000000000000000000]
m : [75078691749480572969 / 50000000000000000000, 65349035271984301417 / 50000000000000000000, 197749684713448959 / 390625000000000000]
g : [55004517159953749153 / 50000000000000000000, -16855100105496833681 / 100000000000000000000, -3071542002180356553 / 10000000000000000000]
d : [6402444114143491529 / 25000000000000000000, 1512405669161048861 / 3125000000000000000, 138455422891693366717 / 100000000000000000000]
n : [219645386246014372617 / 100000000000000000000, 2060337546449996283 / 2500000000000000000, 103915605591948981311 / 100000000000000000000]
r : [80669278675267250227 / 100000000000000000000, 89491316625170053671 / 50000000000000000000, -106710761649390571 / 4000000000000000000]
k : [-3570409242653312799 / 5000000000000000000, 31388641911786962043 / 100000000000000000000, 77862725329578499617 / 50000000000000000000]
q : [-8174189264469172221 / 50000000000000000000, 80987165909850807493 / 50000000000000000000, 14602118673630133813 / 100000000000000000000]
c : [-29208463645857193477 / 100000000000000000000, -1237267611881370721 / 100000000000000000000, 71139967501909011721 / 100000000000000000000]
b : [6495632755029997499 / 50000000000000000000, -8465841512559431183 / 25000000000000000000, -13445570934175135761 / 100000000000000000000]
j : [-10969574636258935163 / 25000000000000000000, 19336306514671737893 / 20000000000000000000, 85163819520295574539 / 100000000000000000000]
p : [25851247367218435893 / 100000000000000000000, 129348191109716624881 / 100000000000000000000, -34991666084267913663 / 50000000000000000000]
i : [-922882099221406229 / 50000000000000000000, 8005196442038398953 / 12500000000000000000, 250124049157506711 / 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 = 71428252496984874699970162807802686283773688645383470221161892357272965938580314825256589213807117663636294833167405503 / 142856945705667810268010283289060958898686780662827455750155005587826142641168780000000000000000000000000000000000000000
Collision distance in [70710569 / 100000000, 7071057 / 10000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [57 / 10000, 59 / 10000] ~ [0.0057, 0.0059]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 23906927417256152514730857698366958443325083351745889047106871628596487 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [154618651 / 10000000000000, 154718651 / 10000000000000] ~ [2e-05, 2e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [361 / 1231680576, 3481 / 11085125168] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)