show/hide visualization coordinates
a : (0.915146376661111, 0.42003565858333336, -0.8499483177277778)
b : (0.05221255036111094, 0.05081639408333338, -0.5044673062277778)
c : (0.10276180876111096, 0.42971648468333346, -1.4296013562277778)
d : (0.016589348861110964, 0.23584197068333335, -0.4513577677277778)
e : (0.8334620898611109, 0.22238695628333338, 0.1267698607722222)
f : (1.730745458961111, 0.4115171077833334, -0.27436159322777776)
g : (0.8672508933611109, 0.04679679918333335, 0.07639806897222223)
h : (-0.016540595938889013, -0.23623374331666663, 0.45123875007222225)
i : (-0.833510791938889, -0.22231758321666661, -0.1267223429277778)
j : (-0.778396289238889, 0.1516593577833334, -1.0523315886277778)
k : (-0.867284632138889, -0.0465077255166666, -0.0763399530277778)
l : (-0.052139096038889, -0.05104164631666663, 0.5044155479722222)
m : (0.778488703461111, -0.15225075891666662, 1.0521836460722223)
n : (1.6620601314611112, 0.12542089288333336, 0.6795949257722222)
o : (-0.10259349903888898, -0.43061732421666665, 1.4293351784722221)
p : (-0.915237792438889, -0.41946298321666664, 0.8501140058722223)
q : (-1.730840251338889, -0.41097492771666666, 0.27450835227222226)
r : (-1.662174413638889, -0.12478492951666664, -0.6794281105277777)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['l', 'k', 'd'], ['e', 'a', 'f'], ['j', 'r', 'i'], ['a', 'f', 'g'], ['n', 'f', 'g'], ['q', 'k', 'r'], ['c', 'a', 'd'], ['q', 'p', 'k'], ['n', 'm', 'g'], ['h', 'i', 'b'], ['h', 'p', 'o'], ['q', 'r', 'i'], ['e', 'a', 'd'], ['c', 'j', 'd'], ['q', 'p', 'i'], ['l', 'p', 'o'], ['h', 'g', 'b'], ['l', 'e', 'd'], ['e', 'n', 'f'], ['h', 'm', 'g'], ['h', 'p', 'i'], ['r', 'k', 'j'], ['j', 'i', 'b'], ['c', 'j', 'b'], ['e', 'n', 'm'], ['k', 'j', 'd'], ['l', 'p', 'k'], ['a', 'g', 'b'], ['e', 'm', 'l'], ['l', 'm', 'o'], ['c', 'a', 'b'], ['h', 'm', 'o']]
Coordinate Data:
k : [-1340851633 / 5000000000, 1048311833 / 2000000000, 261784399 / 625000000]
l : [1093950419 / 2000000000, 5196219957 / 10000000000, 4998052697 / 5000000000]
i : [-36624451 / 156250000, 870865147 / 2500000000, 736945297 / 2000000000]
c : [7018761143 / 10000000000, 10003801267 / 10000000000, -292001989 / 312500000]
n : [2261174437 / 1000000000, 6960845349 / 10000000000, 2936974793 / 2500000000]
a : [7571303411 / 5000000000, 4953496503 / 5000000000, -3547533263 / 10000000000]
f : [4659719529 / 2000000000, 4910903749 / 5000000000, 1104166991 / 5000000000]
r : [-10630601081 / 10000000000, 35670297 / 80000000, -1842331191 / 10000000000]
d : [6012731 / 9765625, 8065056127 / 10000000000, 438372237 / 10000000000]
e : [7162881977 / 5000000000, 7930505983 / 10000000000, 3109824261 / 5000000000]
b : [6513268559 / 10000000000, 6214800361 / 10000000000, -23180787 / 2500000000]
q : [-5658629729 / 5000000000, 1596887143 / 10000000000, 7697033437 / 10000000000]
o : [993041613 / 2000000000, 700231589 / 5000000000, 19245301699 / 10000000000]
m : [1377603009 / 1000000000, 4184128831 / 10000000000, 123790291 / 80000000]
j : [-1792819837 / 10000000000, 3611614999 / 5000000000, -1392841493 / 2500000000]
g : [14663651989 / 10000000000, 1543651103 / 2500000000, 1428982651 / 2500000000]
p : [-3161234869 / 10000000000, 378001647 / 2500000000, 13453089973 / 10000000000]
h : [728217137 / 1250000000, 3344298987 / 10000000000, 1892867483 / 2000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 99946353404353398179716014118820970514954267725803757609 / 2997169050689451913745235416888744661518750000000000000000
Collision distance in [9130569 / 50000000, 18261139 / 100000000] ~ [0.18261, 0.18261]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [103 / 1000, 129 / 1250] ~ [0.103, 0.1032]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 979694895614449740521279644976497857 / 5000000000000000000000000000000000000000
rho in [699891 / 50000000, 1399783 / 100000000] ~ [0.014, 0.014]
sigma_min ^ 2 / (16 * E ^ .5) in [265225 / 2771281296, 66564 / 692820323] ~ [0.0001, 0.0001]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)