show/hide visualization coordinates
a : (-0.32186670469942114, -0.013340843011749925, 1.0868924072263715)
b : (-0.5275267564943938, -0.3392732905251308, 0.1641400120771493)
c : (0.3383337285280492, -0.5851174687629795, 0.5998535194455306)
d : (0.650721711679102, 0.043023667936057886, 1.312491197630777)
e : (0.252505733263368, 0.681119173963946, 0.6535085273568062)
f : (-0.6567340583411656, 0.9240852110621407, 0.9915181517460281)
g : (-1.221454018752373, 0.15780345773486554, 0.6850811421815155)
h : (-1.0971940618124507, 0.34633520189406813, -0.2890929924297345)
i : (-0.5140059021353228, -0.2575549195355664, -0.8324237311626962)
j : (0.18636169520303447, -0.7974018990036346, -0.36546498849081954)
k : (1.082229828253248, -0.96132892946138, 0.047509849568873996)
l : (1.25042705422207, -0.6918238669516872, 0.9957064085470426)
m : (0.8878862413058992, -0.026112740104822785, 0.3434849319285859)
n : (0.2816011156656595, 0.4236705596378099, -0.31234532789481373)
o : (-0.4386375934133139, 1.0317584372026458, 0.021548869573406793)
p : (-1.3893788814666528, 1.0767558687882164, 0.3282510611883019)
q : (-1.6124795024576652, 0.8610173136479409, 1.2788734829412347)
r : (-0.43806339625947177, 0.7344483281747833, -0.9332319269277949)
s : (0.29172715515991654, 0.1401969243662486, -1.271271895172041)
t : (0.10506056018321386, -0.8380904851256934, -1.361323695539102)
u : (0.923160795476011, -1.1962531172762823, -0.9113997753649999)
v : (0.9611203971356475, -0.23704202312473238, -0.631269188855015)
w : (1.0062048597570097, -0.47687456152506347, -1.6010360395746077)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['e', 'n', 'm'], ['h', 'p', 'g'], ['h', 'i', 'r'], ['h', 'i', 'b'], ['s', 'i', 't'], ['o', 'n', 'r'], ['w', 's', 't'], ['i', 'b', 'j'], ['s', 'n', 'r'], ['o', 'p', 'f'], ['m', 'd', 'l'], ['e', 'm', 'd'], ['w', 'u', 't'], ['c', 'b', 'j'], ['q', 'g', 'f'], ['u', 'k', 'j'], ['h', 'g', 'b'], ['v', 'k', 'm'], ['q', 'p', 'f'], ['k', 'c', 'j'], ['a', 'g', 'f'], ['a', 'c', 'b'], ['h', 'o', 'r'], ['h', 'p', 'o'], ['v', 'u', 'k'], ['m', 'k', 'l'], ['e', 'a', 'd'], ['l', 'd', 'c'], ['w', 'v', 'u'], ['t', 'u', 'j'], ['v', 's', 'w'], ['b', 'a', 'g'], ['i', 'j', 't'], ['o', 'e', 'f'], ['a', 'd', 'c'], ['l', 'k', 'c'], ['q', 'p', 'g'], ['o', 'e', 'n'], ['s', 'v', 'n'], ['v', 'm', 'n'], ['e', 'a', 'f'], ['s', 'i', 'r']]
Coordinate Data:
i : [-2632551422393502181 / 100000000000000000000, 4347374036686824417 / 20000000000000000000, -34453746257295631947 / 100000000000000000000]
q : [-112479911454627741731 / 100000000000000000000, 5343763740071394641 / 4000000000000000000, 2208449689413718233 / 1250000000000000000]
f : [-3381073408595556671 / 20000000000000000000, 6995044162160242119 / 5000000000000000000, 36985110508394196589 / 25000000000000000000]
j : [33702104155721113177 / 50000000000000000000, -1289913110534907461 / 4000000000000000000, 6121064004946016121 / 50000000000000000000]
d : [56920104979524493813 / 50000000000000000000, 5179472893059655093 / 10000000000000000000, 180037746622051672209 / 100000000000000000000]
c : [41300705821971852483 / 50000000000000000000, -344355773103349607 / 3125000000000000000, 108773978803527035459 / 100000000000000000000]
s : [77940754307130428603 / 100000000000000000000, 61512054573615631991 / 100000000000000000000, -78338562658230104309 / 100000000000000000000]
o : [2452139724903694369 / 50000000000000000000, 37667051464313838963 / 25000000000000000000, 50943513816314669497 / 100000000000000000000]
e : [74018612117475582239 / 100000000000000000000, 23120855906677074619 / 20000000000000000000, 114139479594654593903 / 100000000000000000000]
l : [86905372106672886963 / 50000000000000000000, -21690024558177948979 / 100000000000000000000, 9272454232104890631 / 6250000000000000000]
u : [141084118338739891103 / 100000000000000000000, -72132949590637463837 / 100000000000000000000, -21175675338763004369 / 50000000000000000000]
v : [144880078504703530721 / 100000000000000000000, 148675998903234557 / 625000000000000000, -14338292026527516563 / 100000000000000000000]
p : [-90169849355526510493 / 100000000000000000000, 155167949015812418169 / 100000000000000000000, 81613732977804171759 / 100000000000000000000]
k : [39247755404115897683 / 25000000000000000000, -9728106161829446347 / 20000000000000000000, 10707922363172277133 / 20000000000000000000]
t : [59274094809460165409 / 100000000000000000000, -3631668637557856983 / 10000000000000000000, -43671871347468102733 / 50000000000000000000]
h : [-7618920923763287433 / 12500000000000000000, 5132867645399848943 / 6250000000000000000, 19879327616000534831 / 100000000000000000000]
r : [2480849582595800833 / 50000000000000000000, 120937194954469114647 / 100000000000000000000, -44534565833805498019 / 100000000000000000000]
w : [37347131191709939039 / 25000000000000000000, -24386751939447419 / 12500000000000000000, -55657488549243391037 / 50000000000000000000]
a : [16581368321196665129 / 100000000000000000000, 23079138917907887683 / 50000000000000000000, 39369466895402785383 / 25000000000000000000]
b : [-1992318429150304867 / 50000000000000000000, 3391258271119422507 / 25000000000000000000, 65202628066688918737 / 100000000000000000000]
m : [137556662921728689911 / 100000000000000000000, 11220272031627122861 / 25000000000000000000, 41568560025916291361 / 50000000000000000000]
g : [-73377363084098529001 / 100000000000000000000, 12654541582095463907 / 20000000000000000000, 58648370538562761891 / 50000000000000000000]
n : [76928150357704724463 / 100000000000000000000, 1797188362015435157 / 2000000000000000000, 702163762779704761 / 4000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 23
|E| = 63
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 61639034450922700663500094628135548574395488933746779783066918212366145941112546782896806346917519274925550213180561 / 152255475715451545774839522975021647725137749920481795745847184679896678871806467187500000000000000000000000000000000
Collision distance in [318135004712026722735872539851 / 500000000000000000000000000000, 636270009424053445471745079703 / 1000000000000000000000000000000] ~ [0.63627, 0.63627]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [803 / 5000, 201 / 1250] ~ [0.1606, 0.1608]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 7756232212397461998347806847618304354762801 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [557000258972918683089139170561 / 2000000000000000000000000000000000000000000000000, 557000258974918683089139170561 / 2000000000000000000000000000000000000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [806011250000000000000000000 / 3968626966596885885752423630459, 538680000000000000000000000 / 2645751311064590590501615753639] ~ [0.0002, 0.0002]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-12499999999993126473108951 / 62500000000000000000000000000, 100000000000055056693603221 / 500000000000000000000000000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [7937253933193771771504847260917 / 125000000000000000000000000000, 3968626966596885885752423630459 / 62500000000000000000000000000] ~ [63.49803, 63.49803]
LHS := (LHS NUM) / (LHS DEN) in [-8333333333328750982072634 / 2645751311064590590501615753639, 33333333333351685564534407 / 10583005244258362362006463014556] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [636270009424053445471745079702 / 4795831523312719541597438064163, 636270009424053445471745079703 / 4795831523312719541597438064162] ~ [0.13267, 0.13267]
Success: LHS < CD / |V| ^ .5
Success: existence proven