show/hide visualization coordinates
a : (0.7078801606722973, 0.0016097100848206924, -0.2985663678612559)
b : (0.036000524455907235, 0.02183828020451395, -1.0389504299456878)
c : (0.4394940138115312, 0.8742855601355906, -0.7064949607686389)
d : (0.3796191851250945, 0.7456366500811991, 0.2833860739176444)
e : (1.0870068888509214, 0.12342281104436881, 0.6187255662661464)
f : (0.7167147368950129, -0.764108165748609, 0.3445495508440001)
g : (0.0036936998657398634, -0.7062224608705615, -0.35419950706196346)
h : (-0.7486091916809234, -0.5971616943670209, -1.0039272258643783)
i : (-0.6700696907462171, 0.06908126984338964, -1.7455146175000862)
j : (-0.39436155740641565, 0.8975155903087408, -1.2579886162597482)
k : (-0.4499041667606115, 0.7242714436254617, -0.2746771273682018)
l : (-0.46710470554775607, 0.37024459780345137, 0.6603999464084739)
m : (0.35363674304335946, 0.42232292237418934, 1.2293211383801408)
n : (1.2057096833753347, 0.06287657116465839, 1.6098077018172434)
o : (1.4439657828807113, -0.7156736251426198, 1.0292100589711992)
p : (0.4927398138177451, -0.5655218164503087, 1.2986977027076954)
q : (-0.2330090052706546, -0.6007454613099114, 0.6116402477342427)
r : (-0.8118809277522381, -0.18999429543416857, -0.09276785634619267)
s : (-1.1259102245111274, 0.32216375287672605, -0.8921924833921028)
t : (-1.5611510613828383, -0.3241647461416969, -1.5189499207439106)
u : (-0.40446070173487403, -0.17167689408221365, 1.4984911260653813)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['k', 'r', 'l'], ['g', 'b', 'h'], ['k', 'r', 's'], ['q', 'g', 'f'], ['j', 's', 'i'], ['n', 'p', 'm'], ['a', 'b', 'c'], ['b', 'j', 'i'], ['b', 'j', 'c'], ['a', 'd', 'c'], ['n', 'e', 'm'], ['t', 'h', 's'], ['p', 'u', 'm'], ['t', 'h', 'i'], ['g', 'a', 'b'], ['q', 'r', 'l'], ['m', 'l', 'u'], ['q', 'p', 'u'], ['d', 'k', 'l'], ['a', 'e', 'd'], ['a', 'f', 'e'], ['b', 'h', 'i'], ['t', 's', 'i'], ['g', 'h', 'r'], ['h', 'r', 's'], ['o', 'f', 'e'], ['q', 'p', 'f'], ['k', 'j', 's'], ['p', 'n', 'o'], ['k', 'j', 'c'], ['g', 'a', 'f'], ['q', 'l', 'u'], ['g', 'r', 'q'], ['d', 'l', 'm'], ['p', 'f', 'o'], ['d', 'k', 'c'], ['o', 'n', 'e'], ['d', 'e', 'm']]
Coordinate Data:
g : [5164275822526704131 / 10000000000000000000, 117761299400989374021 / 100000000000000000000, 44956218271816355491 / 50000000000000000000]
s : [82301575331476883943 / 50000000000000000000, 7461339013130311807 / 50000000000000000000, 71855867088323327259 / 50000000000000000000]
l : [9872259876661662847 / 10000000000000000000, 5057296766794047571 / 50000000000000000000, -11547508803411018917 / 100000000000000000000]
o : [-46192225038115048617 / 50000000000000000000, 29676603957048800579 / 25000000000000000000, -24214260029841777343 / 50000000000000000000]
e : [-56688560673251136309 / 100000000000000000000, 8699193052374088247 / 25000000000000000000, -1476014157835654107 / 20000000000000000000]
j : [91448283952482585031 / 100000000000000000000, -42612505716940853763 / 100000000000000000000, 36058269492682235347 / 20000000000000000000]
c : [322509073227516203 / 4000000000000000000, -40289502699625826131 / 100000000000000000000, 125141981914300262171 / 100000000000000000000]
u : [18491639677065686439 / 20000000000000000000, 64306742722154602003 / 100000000000000000000, -95356626769101761491 / 100000000000000000000]
d : [14050209699331573019 / 100000000000000000000, -13712305847093334353 / 50000000000000000000, 26153878445671925901 / 100000000000000000000]
k : [24250636221975543727 / 25000000000000000000, -25288091048612936269 / 100000000000000000000, 81960198574256543839 / 100000000000000000000]
r : [133200220987064840943 / 100000000000000000000, 1653462071433752357 / 2500000000000000000, 15942317868013907331 / 25000000000000000000]
f : [-19659345477660267593 / 100000000000000000000, 15443733736099266113 / 12500000000000000000, 5009382688259089813 / 25000000000000000000]
q : [37656514369453239739 / 50000000000000000000, 268033998612310921 / 250000000000000000, -1667884733996977867 / 25000000000000000000]
i : [23803819457292548929 / 20000000000000000000, 8046185265918853719 / 20000000000000000000, 28630493448430620621 / 12500000000000000000]
p : [1369073415033256621 / 50000000000000000000, 51845617479482055389 / 50000000000000000000, -4711080277083323599 / 6250000000000000000]
a : [-9387943927694356461 / 50000000000000000000, 23489041152725581111 / 50000000000000000000, 42174561311780978549 / 50000000000000000000]
n : [-34279420062846226761 / 50000000000000000000, 40851396197467395487 / 100000000000000000000, -53244142172143997909 / 50000000000000000000]
t : [208127234350124859373 / 100000000000000000000, 9944440991012864757 / 12500000000000000000, 103193738955913713283 / 50000000000000000000]
m : [16648453907505074951 / 100000000000000000000, 2453380538257149073 / 50000000000000000000, -8554953500072212109 / 12500000000000000000]
h : [126873047379933367821 / 100000000000000000000, 2671380568765883367 / 2500000000000000000, 154885208423874179633 / 100000000000000000000]
b : [24206037883125151499 / 50000000000000000000, 2247761264674091773 / 5000000000000000000, 158387528832005144643 / 100000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 21
|E| = 57
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 500000000000000000001470872268755220117150544133923387889184305852824312579036955338633181354406203725963304673279622289 / 1000000000000000000012332947504074544191501423662279564246471283050879197222634780000000000000000000000000000000000000000
Collision distance in [353553390593273762198762035227 / 500000000000000000000000000000, 141421356237309504879504814091 / 200000000000000000000000000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5427 / 10000, 5429 / 10000] ~ [0.5427, 0.5429]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 496054804008420514950622099787828884255743 / 20000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [49215267932800749872393209907 / 312500000000000000000000000000000000000000000000, 49215267933113249872393209907 / 312500000000000000000000000000000000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [18407705625000000000000000000 / 7549834435270749697236684806947, 9210637812500000000000000000 / 3774917217635374848618342403473] ~ [0.00244, 0.00244]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-99999999999991239529941747 / 500000000000000000000000000000, 200000000000017527397068937 / 1000000000000000000000000000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [3774917217635374848618342403473 / 62500000000000000000000000000, 7549834435270749697236684806947 / 125000000000000000000000000000] ~ [60.39868, 60.39868]
LHS := (LHS NUM) / (LHS DEN) in [-33333333333330413176647249 / 10066445913694332929648913075928, 200000000000017527397068937 / 60398675482165997577893478455568] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [707106781186547524397524070454 / 4582575694955840006588047193729, 707106781186547524397524070455 / 4582575694955840006588047193728] ~ [0.1543, 0.1543]
Success: LHS < CD / |V| ^ .5
Success: existence proven