show/hide visualization coordinates
a : (0.27202597825877284, -0.7333785003574865, -0.17565327764870348)
b : (-0.2751815301023892, -0.16160745070465687, -0.7869157495640586)
c : (0.723239379104115, -0.1307120586157815, -0.8338323010883544)
d : (1.0857576014014836, -0.218474293301119, 0.09400299068782697)
e : (0.3162332297157948, -0.30478337333444405, 0.7267612257867841)
f : (-0.3177012986320755, -1.0605687476156453, 0.5627018408342996)
g : (-0.6802195209294439, -0.9728065129303078, -0.3651334509418817)
h : (-1.180219520929444, -0.10678110914586925, -0.3651334509418817)
i : (-0.5363504215311714, 0.6521186631784295, -0.26764643433872076)
j : (0.19096850354950878, 0.7076168088066082, -0.9516984331307115)
k : (1.0588906454045437, 0.5942609522505014, -1.4352908291236592)
l : (1.4214088677019119, 0.5064987175651638, -0.5074555373474777)
m : (1.7839270899992805, 0.41873648287982634, 0.4203797544287036)
n : (0.8260220260435693, 0.5538763542560048, 0.6736683321664982)
o : (-0.173832199233803, 0.564356428493092, 0.6601888574374606)
p : (-0.6311759317580825, -0.23969937190235857, 1.0400980310187147)
q : (-1.0548623756367872, -1.1241995662215913, 1.2354162419532222)
r : (-1.180219520929444, -1.5039742110938241, 0.31887011368894064)
s : (-1.680219520929444, -0.9728065129303078, -0.3651334509418817)
t : (-1.4143891727360227, -0.5489334668289257, 0.5006990194402934)
u : (-1.1473708923957344, 0.4146678302054989, 0.4875165190063894)
v : (0.3408752592738431, 1.0703513742264321, -0.03194216126413901)
w : (0.9449375514968319, 1.3420018989030504, -0.7811515709469236)
x : (1.3074557737942, 1.254239664217713, 0.1466837208292578)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['w', 'k', 'l'], ['w', 'j', 'v'], ['f', 'a', 'g'], ['m', 'd', 'l'], ['w', 'k', 'j'], ['a', 'e', 'd'], ['s', 'r', 'g'], ['b', 'a', 'g'], ['b', 'i', 'j'], ['k', 'j', 'c'], ['b', 'h', 'g'], ['f', 'p', 'e'], ['s', 'r', 't'], ['n', 'x', 'v'], ['f', 'a', 'e'], ['i', 'j', 'v'], ['u', 't', 'h'], ['u', 'p', 't'], ['k', 'c', 'l'], ['f', 'r', 'g'], ['p', 'e', 'o'], ['s', 't', 'h'], ['u', 'p', 'o'], ['b', 'c', 'j'], ['f', 'q', 'r'], ['u', 'i', 'h'], ['u', 'i', 'o'], ['i', 'v', 'o'], ['q', 'p', 't'], ['a', 'd', 'c'], ['m', 'n', 'd'], ['w', 'x', 'l'], ['m', 'n', 'x'], ['n', 'e', 'd'], ['b', 'a', 'c'], ['n', 'e', 'o'], ['n', 'o', 'v'], ['q', 'r', 't'], ['w', 'x', 'v'], ['m', 'x', 'l'], ['s', 'h', 'g'], ['d', 'c', 'l'], ['b', 'i', 'h'], ['f', 'q', 'p']]
Coordinate Data:
s : [-88561469947326249423479926209 / 25000000000000000000000000000000000000000000000000000000000, -72838168422847660960963768099 / 200000000000000000000000000000000000000000000000000000000000, -175827961386003563120622890463 / 2500000000000000000000000000000000000000000000000000000000000000000000000000000000000]
v : [2526368475254108573794265801 / 1250000000000000000000000000, 102157894357837003732950691557 / 50000000000000000000000000000, 66638257935548536156248356881 / 200000000000000000000000000000]
r : [99999999999999999999999999993 / 200000000000000000000000000000, -265583849081758200953963966657 / 500000000000000000000000000000, 136800712926164465131642472449 / 200000000000000000000000000000]
k : [54782203326679751543404260133 / 20000000000000000000000000000, 78353373259040456932364213767 / 50000000000000000000000000000, -107015737818177737933263290109 / 100000000000000000000000000000]
h : [249999999999999999999999999999 / 500000000000000000000000000000, 866025403784438646763723170757 / 1000000000000000000000000000000, 288292317871358898585831170441 / 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
m : [173207330546436216667291913083 / 50000000000000000000000000000, 139154299581013409079275963731 / 100000000000000000000000000000, 196378301342646320642731150859 / 250000000000000000000000000000]
d : [69149428058273185597923266609 / 25000000000000000000000000000, 754332219629188817734961157337 / 1000000000000000000000000000000, 28696027601856791033460728789 / 62500000000000000000000000000]
p : [52452179458568066659231653343 / 50000000000000000000000000000, 146621428205589844449076210169 / 200000000000000000000000000000, 70261574098029818292351241889 / 50000000000000000000000000000]
o : [150638732169564089368996067879 / 100000000000000000000000000000, 153716294142339987896587132011 / 100000000000000000000000000000, 102532230837934228238034005263 / 100000000000000000000000000000]
g : [100000000000000000000000000001 / 100000000000000000000000000000, -8602493493726816858044034717 / 2500000000000000000000000000000000000000000000000000000000, 24777135358232222466329949909 / 400000000000000000000000000000000000000000000000000000000000000000000000000000000000]
a : [97612274959410836014435025369 / 50000000000000000000000000000, 47885602514564269762057129249 / 200000000000000000000000000000, 189480173293178227502389137599 / 1000000000000000000000000000000]
w : [262515707242627573657419186579 / 100000000000000000000000000000, 231480841183335826664604118181 / 100000000000000000000000000000, -26001132500315114404912813661 / 62500000000000000000000000000]
t : [132915174096710571013045153479 / 500000000000000000000000000000, 105968261525345530281046908833 / 250000000000000000000000000000, 432916235191087533317457304603 / 500000000000000000000000000000]
l : [310162838863135595525802563423 / 100000000000000000000000000000, 36982630762386790368000548909 / 25000000000000000000000000000, -142322086405596048380854148851 / 1000000000000000000000000000000]
n : [250624154697301320342069002039 / 100000000000000000000000000000, 19083535839828909161671989921 / 12500000000000000000000000000, 103880178310837996964732709533 / 100000000000000000000000000000]
x : [29876752947236441146620044933 / 10000000000000000000000000000, 222704617714802074271877886279 / 100000000000000000000000000000, 127954292942784875118293433421 / 250000000000000000000000000000]
f : [136251822229736837808781262749 / 100000000000000000000000000000, -87762234685337523927262318987 / 1000000000000000000000000000000, 927835291776181330951778752267 / 1000000000000000000000000000000]
e : [199645275064523875786532572249 / 100000000000000000000000000000, 334011569797931916754976221551 / 500000000000000000000000000000, 54594733836433292461088365927 / 50000000000000000000000000000]
b : [35125949770676368021265720691 / 25000000000000000000000000000, 16223981244513019574716181707 / 20000000000000000000000000000, -210891149311088424810752702303 / 500000000000000000000000000000]
i : [14298363742478406445026850641 / 12500000000000000000000000000, 16249251761087374028931336391 / 10000000000000000000000000000, 19497403320632190285712260071 / 200000000000000000000000000000]
u : [266424314266854756254128645643 / 500000000000000000000000000000, 27749486862716133430876308003 / 20000000000000000000000000000, 53290623121766946196130715889 / 62500000000000000000000000000]
q : [625357145292656769078338906439 / 1000000000000000000000000000000, -30278610658256705597346218009 / 200000000000000000000000000000, 160054969289510403874047442687 / 100000000000000000000000000000]
c : [240345890003355904582911803687 / 100000000000000000000000000000, 42104722715726317083111173817 / 50000000000000000000000000000, -93739770029294534883281418327 / 200000000000000000000000000000]
j : [46779700611973816311827651117 / 25000000000000000000000000000, 168042332173691588781075816653 / 100000000000000000000000000000, -73320622773603704079425064499 / 125000000000000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 24
|E| = 66
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 62472155564008107771957757234327921639255541080546778538760741070759617639363690585567007800550280219391384896322602289 / 105018286019198714958505197450022464795874673753203735046401294638697177825574940000000000000000000000000000000000000000
Collision distance in [385638857001463529244629892883 / 500000000000000000000000000000, 771277714002927058489259785767 / 1000000000000000000000000000000] ~ [0.77128, 0.77128]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [47588371546520969999 / 100000000000000000000, 47588371546520970001 / 100000000000000000000] ~ [0.47588, 0.47588]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 42806764704158082000372668037363990158600145327310853069127694226207266525479681426597811202913952768157737016536819192832854692407986898678077760353797710335594347898719709273857748819953909216992623447811171954061776820094184925360981634934998574132812512938275909804581187602376077907 / 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [1462989485679204770414776522373 / 500000000000000000000000000000000000000000000000000000000, 1463489485679204770414776522373 / 500000000000000000000000000000000000000000000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [2264653106449726657869733906647858060001 / 1299846144741753657673581370922720000000000, 2264653106449726658060087392833941940001 / 1299846144741753657673581370922560000000000] ~ [0.00174, 0.00174]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-3479030001 / 100000000000000000000, 6520970001 / 100000000000000000000] ~ [-0.0, 0.0]
LHS DEN := 8 * |E| ^ .5 in [4062019202317980180229941784133 / 62500000000000000000000000000, 8124038404635960360459883568267 / 125000000000000000000000000000] ~ [64.99231, 64.99231]
LHS := (LHS NUM) / (LHS DEN) in [-2174393750625000000 / 4062019202317980180229941784133, 313508173125000000 / 312463015562921552325380137241] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [385638857001463529244629892883 / 2449489742783178098197284074706, 771277714002927058489259785767 / 4898979485566356196394568149411] ~ [0.15744, 0.15744]
Success: LHS < CD / |V| ^ .5
Success: existence proven