show/hide visualization coordinates
a : (-0.30739818166807714, 0.33798029764114307, 0.24336137311557615)
b : (0.34782011426336024, 1.068762485439909, 0.051924781095643135)
c : (-0.3849981365810276, 0.8710537327368228, -0.5991423709519845)
d : (-1.0390555515751794, 0.13899689732662196, -0.4086227702858593)
e : (-0.9602989510937208, -0.39534987311639014, 0.4329637926628249)
f : (-0.2274822300272314, -0.19764010214168326, 1.084031651262997)
g : (0.4265767742424955, 0.5344176321381604, 0.8935111268178718)
h : (0.6429015967072728, 0.11411225885868209, 0.01229115651913848)
i : (0.5621679249067002, 0.6478611283975754, -0.8294910865295528)
j : (0.26906194737321065, 1.6031100353524756, -0.7896633239347761)
k : (-0.09239696153314653, -0.0842659436653469, -0.6409819028653796)
l : (-0.7459506272883536, -0.8162514274466108, -0.4484514639610783)
m : (-1.6931162919836944, -0.5930592295792987, -0.21810329324009442)
n : (-0.01336989576959563, -0.62039841276138, 0.203443699820143)
o : (0.7196826278368971, -0.4208326489535388, 0.8536826073528073)
p : (0.505334613498524, 6.996277666093675e-05, 1.7350996112722743)
q : (0.9340321344009747, -0.8417347257129861, -0.027733195498452157)
r : (0.8552749398735003, -0.30738751738147474, -0.8693206301036038)
s : (0.20121415441709284, -1.0394445499093405, -0.6787997625484943)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['o', 'n', 'q'], ['h', 'g', 'b'], ['c', 'j', 'b'], ['h', 'o', 'g'], ['f', 'p', 'g'], ['e', 'a', 'f'], ['s', 'n', 'l'], ['r', 's', 'q'], ['e', 'l', 'm'], ['e', 'f', 'n'], ['h', 'o', 'q'], ['r', 'h', 'q'], ['e', 'n', 'l'], ['r', 'i', 'h'], ['i', 'r', 'k'], ['s', 'k', 'l'], ['d', 'a', 'c'], ['r', 's', 'k'], ['e', 'd', 'a'], ['a', 'g', 'b'], ['d', 'm', 'l'], ['s', 'n', 'q'], ['a', 'c', 'b'], ['o', 'f', 'p'], ['a', 'f', 'g'], ['i', 'c', 'j'], ['i', 'c', 'k'], ['e', 'd', 'm'], ['d', 'c', 'k'], ['i', 'j', 'b'], ['i', 'h', 'b'], ['o', 'g', 'p'], ['n', 'o', 'f'], ['d', 'k', 'l']]
Coordinate Data:
n : [4954772842441756853 / 10000000000000000000, 111772653081209772517 / 100000000000000000000, 5100818417046361501 / 20000000000000000000]
l : [122805801576293361451 / 100000000000000000000, 131357954549732864827 / 100000000000000000000, 90693608463353939197 / 100000000000000000000]
m : [108761184022913716263 / 50000000000000000000, 54519367381500825013 / 50000000000000000000, 67658791391255549911 / 100000000000000000000]
e : [144240633956830087087 / 100000000000000000000, 89267799116710803639 / 100000000000000000000, 1276041400481805213 / 50000000000000000000]
r : [-3731675513989202607 / 10000000000000000000, 402357817716096319 / 500000000000000000, 132780525077606495123 / 100000000000000000000]
i : [-800605364321201619 / 10000000000000000000, -602132041387430039 / 4000000000000000000, 128797570720201382397 / 100000000000000000000]
j : [21304544110136938093 / 100000000000000000000, -13822273966271971413 / 12500000000000000000, 124814794460723723279 / 100000000000000000000]
d : [152116294004975941427 / 100000000000000000000, 17916561036204796311 / 50000000000000000000, 43355369547916016193 / 50000000000000000000]
h : [-8039710411634632623 / 50000000000000000000, 38321585919203577617 / 100000000000000000000, 2230967320766612833 / 5000000000000000000]
s : [3511165425718590507 / 12500000000000000000, 153677266796005849543 / 100000000000000000000, 113728438322095542563 / 100000000000000000000]
o : [-4751504787246338789 / 20000000000000000000, 91816076700425667793 / 100000000000000000000, -39519798668034630277 / 100000000000000000000]
p : [-1161361251197201139 / 50000000000000000000, 1553931735231427963 / 3125000000000000000, -31915374764995329423 / 25000000000000000000]
f : [35479480925090575627 / 50000000000000000000, 17374205504810029239 / 25000000000000000000, -62554703059053607213 / 100000000000000000000]
q : [-72307959348223137 / 160000000000000000, 1046142846690393767 / 781250000000000000, 47482208610440741 / 97656250000000000]
b : [107429819368975889 / 800000000000000000, -57143436738919101273 / 100000000000000000000, 40655983957681790203 / 100000000000000000000]
c : [43355276252780381411 / 50000000000000000000, -934314036715262533 / 2500000000000000000, 105762699162444558203 / 100000000000000000000]
a : [78950557014265720747 / 100000000000000000000, 15934782040957479041 / 100000000000000000000, 4302464951137697659 / 20000000000000000000]
g : [2776530711604227079 / 50000000000000000000, -927237852186062157 / 25000000000000000000, -1740106024581643093 / 4000000000000000000]
k : [11490087000154531789 / 20000000000000000000, 29079703085803236143 / 50000000000000000000, 109946652353784064901 / 100000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 4999983622905316103273517373716658172985897735200660943345811167795713807777732146991676552814548043446894999242479801 / 9999997089110627432237258966047143101722928039859073330905409940552563710366011600000000000000000000000000000000000000
Collision distance in [17677643 / 25000000, 70710573 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [61 / 10000, 63 / 10000] ~ [0.0061, 0.0063]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 27138879054011587072425455709862277299726326090111884508205509439212029 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [8236941 / 500000000000, 8241941 / 500000000000] ~ [2e-05, 2e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [3721 / 11426285488, 189 / 544108832] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)