show/hide visualization coordinates
a : (-0.2083085333642858, -0.4018907781357142, -0.11851288144285715)
b : (-0.35625708596428574, -0.5663101245357143, 0.8571066662571428)
c : (-1.0351194189642858, -0.05830518843571425, 0.32768047085714286)
d : (-0.8693460773642857, 0.14052936726428572, -0.637790787642857)
e : (-0.02468074826428579, -0.16866671253571425, -1.073880360442857)
f : (0.6541967754357142, -0.6766704438357143, -0.5444729994428572)
g : (0.4883688759357142, -0.8754884731357142, 0.42102537215714286)
h : (0.4866951895357142, -0.04059771163571424, 0.9714568483571429)
i : (-0.3929138204642858, 0.4312049748642857, 0.9175718979571428)
j : (-0.6891372749642858, 0.8392757591642858, 0.05450759655714282)
k : (-0.10573631666428573, 0.7755702875642858, -0.754701790242857)
l : (0.7738664248357142, 0.3037567797642857, -0.700807300642857)
m : (1.0700659049357142, -0.10431328943571422, 0.16226548015714282)
n : (0.2083061053357142, 0.40190555306428577, 0.11855178755714285)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['a', 'f', 'g'], ['n', 'j', 'k'], ['j', 'i', 'n'], ['a', 'd', 'c'], ['c', 'd', 'j'], ['c', 'i', 'j'], ['n', 'h', 'i'], ['e', 'd', 'k'], ['a', 'b', 'c'], ['b', 'h', 'g'], ['m', 'n', 'h'], ['m', 'g', 'h'], ['c', 'b', 'i'], ['f', 'm', 'g'], ['e', 'a', 'd'], ['f', 'l', 'm'], ['b', 'h', 'i'], ['d', 'j', 'k'], ['n', 'l', 'k'], ['a', 'b', 'g'], ['e', 'a', 'f'], ['e', 'f', 'l'], ['m', 'l', 'n'], ['e', 'l', 'k']]
Coordinate Data:
l : [-2189670359 / 10000000000, 1373505809 / 10000000000, 11410347571 / 10000000000]
a : [7632079223 / 10000000000, 2107495347 / 2500000000, 5587403379 / 10000000000]
g : [66530513 / 1000000000, 6582979169 / 5000000000, 192020843 / 10000000000]
i : [4739066047 / 5000000000, 49511929 / 5000000000, -954688883 / 2000000000]
h : [341020997 / 5000000000, 4817050723 / 10000000000, -5312293919 / 10000000000]
n : [866483209 / 2500000000, 98004519 / 2500000000, 3216756689 / 10000000000]
m : [-128791629 / 250000000, 5454206501 / 10000000000, 2779619763 / 10000000000]
e : [1448950343 / 2500000000, 1524435183 / 2500000000, 15141078169 / 10000000000]
b : [9111564749 / 10000000000, 2518543713 / 2500000000, -2084396049 / 5000000000]
c : [15900188079 / 10000000000, 4994125491 / 10000000000, 35170933 / 312500000]
f : [-198594773 / 2000000000, 2235555609 / 2000000000, 9847004559 / 10000000000]
k : [103224329 / 156250000, -3344629269 / 10000000000, 11949292467 / 10000000000]
d : [14242454663 / 10000000000, 1502889967 / 5000000000, 10780182441 / 10000000000]
j : [12440366639 / 10000000000, -796336797 / 2000000000, 3857198599 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 14
|E| = 36
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 1350943040033964753225490225266922452227678847066194541889 / 2101997553145884727890815660983148294836500000000000000000
Collision distance in [20042063 / 25000000, 80168253 / 100000000] ~ [0.80168, 0.80168]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [69 / 500, 691 / 5000] ~ [0.138, 0.1382]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 6202050862947865413085015291165401 / 400000000000000000000000000000000000000
rho in [78753 / 20000000, 196883 / 50000000] ~ [0.00394, 0.00394]
sigma_min ^ 2 / (16 * E ^ .5) in [119025 / 600000001, 477481 / 2400000000] ~ [0.0002, 0.0002]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)