show/hide visualization coordinates
a : (-0.48809349957195625, 0.23640997650852325, -0.2883466029516523)
b : (0.11113268480752891, 0.5968970365738635, -1.0031736821571626)
c : (-0.2794529728196293, -0.3192618279852532, -1.0931425381275957)
d : (-0.8772103554749817, -0.6804593066619722, -0.37744631963116004)
e : (-1.0843830045502159, -0.12549817775104855, 0.42821653547768346)
f : (-0.6937971193470629, 0.7906613142475332, 0.5181856899913441)
g : (-0.09603964197604498, 1.151858131573125, -0.1975098601599864)
h : (0.5017189669893632, 1.5130565582797464, -0.9132065327375356)
i : (0.8211009762958582, 0.7730120358196977, -0.3213191941734048)
j : (0.4319024613132898, -0.14360765279220272, -0.41261182281093267)
k : (0.03993043685139985, -1.059304460779813, -0.5012572597440563)
l : (-0.6700389025878368, -1.235421694853441, -1.1831117168012164)
m : (-0.1677653439034964, -0.5059204516827149, 0.30535960911619786)
n : (-0.37441512005453303, 0.050618413426986475, 1.1100727210776187)
o : (-1.2915558068177422, 0.4294634898555457, 1.2338816332518263)
p : (0.22399358464193997, 0.4130144519180099, 0.39552421424656337)
q : (1.1404831323682743, 0.032970523059859536, 0.2705677308963995)
r : (0.7498984904257601, -0.8831878866806311, 0.1805987768492805)
s : (0.5427257092132988, -0.3282273296120536, 0.9862637477852197)
t : (1.4598653241967865, -0.7070731424637604, 0.8624548706025711)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['a', 'f', 'g'], ['p', 'f', 'n'], ['k', 'r', 'j'], ['c', 'k', 'j'], ['e', 'n', 'o'], ['p', 'q', 'i'], ['b', 'j', 'i'], ['a', 'c', 'b'], ['p', 'f', 'g'], ['k', 'l', 'd'], ['t', 'q', 's'], ['c', 'l', 'd'], ['k', 'm', 'd'], ['q', 'j', 'i'], ['t', 'r', 's'], ['n', 's', 'm'], ['b', 'c', 'j'], ['f', 'e', 'o'], ['p', 's', 'n'], ['p', 'q', 's'], ['a', 'e', 'd'], ['r', 's', 'm'], ['a', 'g', 'b'], ['a', 'c', 'd'], ['h', 'g', 'i'], ['c', 'k', 'l'], ['q', 'r', 'j'], ['e', 'm', 'd'], ['b', 'h', 'g'], ['b', 'h', 'i'], ['t', 'q', 'r'], ['p', 'g', 'i'], ['k', 'r', 'm'], ['f', 'n', 'o'], ['e', 'n', 'm'], ['a', 'f', 'e']]
Coordinate Data:
b : [2035913864322530901 / 3125000000000000000, 53029749271554313037 / 50000000000000000000, -43963743404096564173 / 100000000000000000000]
k : [29014509431354040489 / 50000000000000000000, -59560651192259021767 / 100000000000000000000, 1556974709303518841 / 25000000000000000000]
m : [37259440787218457363 / 100000000000000000000, -2111125141274605737 / 50000000000000000000, 86889585723239488241 / 100000000000000000000]
a : [5226625220372469379 / 100000000000000000000, 70010792536574603041 / 100000000000000000000, 5503792903290895299 / 20000000000000000000]
f : [-3835934189284550003 / 25000000000000000000, 5017437052419023543 / 4000000000000000000, 108172193810754121279 / 100000000000000000000]
j : [3889048852355883259 / 4000000000000000000, 32009029606502010589 / 100000000000000000000, 3018488506105288103 / 20000000000000000000]
t : [1562675840603490253 / 781250000000000000, -12168759680326875989 / 50000000000000000000, 712995559359384091 / 500000000000000000]
l : [-6483957540607794489 / 50000000000000000000, -77172374599621841583 / 100000000000000000000, -15489386717125483647 / 25000000000000000000]
g : [11108002744990899587 / 25000000000000000000, 80777804021517399769 / 50000000000000000000, 36602638795621069809 / 100000000000000000000]
i : [136146072807153911729 / 100000000000000000000, 123670998467692046673 / 100000000000000000000, 24221705394279226517 / 100000000000000000000]
p : [38217666820881046251 / 50000000000000000000, 876712400775232669 / 1000000000000000000, 2397651155906901169 / 2500000000000000000]
s : [5415427304944899099 / 5000000000000000000, 6773530962258460211 / 50000000000000000000, 154979999590141683113 / 100000000000000000000]
h : [101765499879398859 / 97656250000000000, 197675450713696916589 / 100000000000000000000, -34967028462133851409 / 100000000000000000000]
n : [16594463172114793067 / 100000000000000000000, 51431636228420931877 / 100000000000000000000, 5230028028730674003 / 3125000000000000000]
q : [33616857682879104673 / 20000000000000000000, 49666847191708232903 / 100000000000000000000, 20852599475314914363 / 25000000000000000000]
o : [-1173743836003220883 / 1562500000000000000, 44658071935638425921 / 50000000000000000000, 44935447034200586587 / 25000000000000000000]
e : [-6800290659681686239 / 12500000000000000000, 33819977110617429059 / 100000000000000000000, 99175278359388055113 / 100000000000000000000]
d : [-33685060369930082167 / 100000000000000000000, -541903394511873281 / 2500000000000000000, 9304496424251850229 / 50000000000000000000]
r : [32256456055036023611 / 25000000000000000000, -20974496891170411581 / 50000000000000000000, 1860337562413693793 / 2500000000000000000]
c : [5218135579121033291 / 20000000000000000000, 1805451510899620273 / 12500000000000000000, -52960629001139847863 / 100000000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 31249817929020964829731726081092876343178255579925425923350436349898313652025188649964081902028065063525772894693988641 / 62499864003662736487577285454070274744145275185072765989816379894126421639517556250000000000000000000000000000000000000
Collision distance in [70710549 / 100000000, 1414211 / 2000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [7 / 1250, 29 / 5000] ~ [0.0056, 0.0058]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 4602078417415428110368575562929794140050845509250716006512742674263583 / 20000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [75845883 / 5000000000000, 75895883 / 5000000000000] ~ [2e-05, 2e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [196 / 734846923, 841 / 2939387688] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)