show/hide visualization coordinates
a : (-0.37981493064971145, -0.6384235855824575, -0.8355556607209189)
b : (0.5210762593736511, -0.22368212522407255, -0.9635580089780532)
c : (0.33814162161968664, -0.7821753443031184, -0.1544722939701227)
d : (-0.5627494466524628, -1.1969170940276022, -0.02647011339814276)
e : (-0.452413639231098, -0.20712217168949731, 0.06372685932197131)
f : (-0.26751118126249657, 0.3511214413701631, -0.745084427156531)
g : (0.6333797619275471, 0.7658636180349869, -0.8730862103420964)
h : (0.4524142010781197, 0.20712274662379437, -0.06372803998127763)
i : (0.2675111401395477, -0.3511213676642187, 0.7450845613127647)
j : (0.15520685941851198, -1.3406680682766061, 0.6546131590597152)
k : (-0.7456838793632816, -1.7554105165670164, 0.7826154030583222)
l : (-0.6333797628430125, -0.7658634323149222, 0.873086903594308)
m : (-0.521076490539631, 0.22368204328038388, 0.9635578807269863)
n : (-0.33814172919527746, 0.7821747463253883, 0.15447273538626072)
o : (-0.15520666309048664, 1.3406681280132116, -0.6546131099493717)
p : (0.7456841249011553, 1.7554103875405702, -0.7826156544717038)
q : (0.5627490934073734, 1.196916923295087, 0.026470138053185654)
r : (0.3798146609618659, 0.6384236711659248, 0.8355558784547016)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['l', 'm', 'i'], ['j', 'i', 'c'], ['a', 'd', 'c'], ['l', 'm', 'e'], ['n', 'm', 'e'], ['d', 'l', 'e'], ['h', 'r', 'i'], ['n', 'r', 'q'], ['d', 'l', 'k'], ['j', 'l', 'k'], ['p', 'o', 'q'], ['g', 'p', 'q'], ['a', 'e', 'f'], ['n', 'o', 'q'], ['n', 'e', 'f'], ['d', 'k', 'j'], ['g', 'h', 'q'], ['g', 'o', 'p'], ['g', 'b', 'h'], ['h', 'i', 'c'], ['h', 'r', 'q'], ['j', 'l', 'i'], ['a', 'd', 'e'], ['f', 'g', 'o'], ['a', 'b', 'f'], ['j', 'd', 'c'], ['m', 'r', 'i'], ['a', 'b', 'c'], ['n', 'r', 'm'], ['b', 'h', 'c'], ['f', 'o', 'n'], ['f', 'g', 'b']]
Coordinate Data:
h : [80656028696683399737 / 100000000000000000000, 3868621093354671587 / 5000000000000000000, 46812735709210482153 / 100000000000000000000]
e : [-78614042673906971 / 800000000000000000, 17973965017882131241 / 50000000000000000000, 11911645127907075683 / 20000000000000000000]
f : [2165872615655443749 / 25000000000000000000, 18354458268346061917 / 20000000000000000000, -2132290300831485687 / 10000000000000000000]
l : [-13961683847714907113 / 50000000000000000000, -19926196026778219807 / 100000000000000000000, 70247115033384520187 / 50000000000000000000]
a : [-2566884476099712939 / 100000000000000000000, -1795552838382939369 / 25000000000000000000, -30370026364753637843 / 100000000000000000000]
n : [1600435669343687059 / 100000000000000000000, 67438810918626411019 / 50000000000000000000, 68632813245964317843 / 100000000000000000000]
m : [-16693040465091663071 / 100000000000000000000, 19757087883188096071 / 25000000000000000000, 4673166493126152727 / 3125000000000000000]
k : [-39153779347456734319 / 100000000000000000000, -4755236178079505413 / 4000000000000000000, 65723540006585230409 / 50000000000000000000]
d : [-4172067215274970549 / 20000000000000000000, -31515781099023117563 / 50000000000000000000, 50538528367523970527 / 100000000000000000000]
r : [14679214937011603791 / 20000000000000000000, 60251257160653238299 / 50000000000000000000, 13674112755280840461 / 10000000000000000000]
o : [124337139248892309 / 625000000000000000, 95363480003017578671 / 50000000000000000000, -1534471410949864847 / 12500000000000000000]
g : [49376292390813072831 / 50000000000000000000, 133246509008212681991 / 100000000000000000000, -682461626537427823 / 2000000000000000000]
q : [45844758964804389669 / 50000000000000000000, 88175919767111348517 / 50000000000000000000, 2791627675632840477 / 5000000000000000000]
c : [69228770750840096451 / 100000000000000000000, -21557387225597847473 / 100000000000000000000, 1179322197197686899 / 3125000000000000000]
p : [27495755269746738493 / 25000000000000000000, 4644023719175420201 / 2000000000000000000, -12538012869916064449 / 50000000000000000000]
j : [10187058906144526903 / 20000000000000000000, -15481331924589321693 / 20000000000000000000, 7415428475831860959 / 6250000000000000000]
b : [3500889381049461539 / 4000000000000000000, 17145967341153369451 / 50000000000000000000, -5396282648808384231 / 12500000000000000000]
i : [31082861301413099679 / 50000000000000000000, 21548010438292125803 / 100000000000000000000, 1995218684978354831 / 1562500000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 13888880394257145335984637554682408542922826983037694531349618362943308028522694177317666474597148047563404676387095009 / 27777798972080883407327858875027122247994270160487523331268765471517211631242275000000000000000000000000000000000000000
Collision distance in [70710629 / 100000000, 7071063 / 10000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [17 / 2500, 7 / 1000] ~ [0.0068, 0.007]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 13452817636957025297485097738080651487688574767900478549043360487221587 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [57993141 / 5000000000000, 58043141 / 5000000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [289 / 692820324, 1225 / 2771281292] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)