show/hide visualization coordinates
a : (0.07989223151333336, 1.13241060426, -0.1764470200866668)
b : (-0.2774780538866667, 0.24157782476000006, -0.45700102268666676)
c : (0.13584930131333328, 0.35348038476000004, 0.44802826551333325)
d : (0.4936789246133333, 1.24680768206, 0.7241502901133332)
e : (0.3182235521133333, 0.32798424536000004, 0.36775025351333324)
f : (-0.0953317055866667, 0.21623562266000007, -0.5368881605866668)
g : (-0.33270399838666664, 1.02428215726, -1.0785034144866668)
h : (-0.5957596054866666, 0.11635993806000006, -1.3980679505866669)
i : (-0.4506522059866668, -0.67742945134, -0.8110486357866667)
j : (-0.13240250518666674, -0.55680711354, 0.12928210121333328)
k : (0.3701225235133333, -0.45495383734000006, 0.9878490151133332)
l : (0.6395813527133333, 0.45096443166000005, 1.3078351515133333)
m : (0.05084811971333325, -0.5824833101399999, 0.048942291613333244)
n : (-0.30630442648666667, -1.4752446515399997, -0.2295500738866667)
o : (0.10243649551333328, -1.36318452694, 0.6736689095133332)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['a', 'd', 'e'], ['d', 'e', 'l'], ['o', 'k', 'm'], ['j', 'o', 'n'], ['k', 'e', 'l'], ['b', 'h', 'i'], ['b', 'h', 'g'], ['a', 'b', 'g'], ['h', 'f', 'g'], ['i', 'f', 'm'], ['f', 'e', 'm'], ['i', 'n', 'm'], ['j', 'b', 'i'], ['a', 'b', 'c'], ['a', 'f', 'e'], ['a', 'c', 'd'], ['c', 'd', 'l'], ['l', 'c', 'k'], ['j', 'b', 'c'], ['h', 'i', 'f'], ['o', 'n', 'm'], ['e', 'k', 'm'], ['j', 'i', 'n'], ['a', 'f', 'g'], ['j', 'k', 'o'], ['j', 'c', 'k']]
Coordinate Data:
e : [168813461 / 625000000, 69512241 / 312500000, 1240007463 / 10000000000]
o : [2429442971 / 5000000000, 3827215887 / 2000000000, -1819179097 / 10000000000]
m : [53747697 / 100000000, 11329067267 / 10000000000, 2214043541 / 5000000000]
h : [1480105869 / 1250000000, 868126957 / 2000000000, 295284211 / 156250000]
g : [9210290881 / 10000000000, -4738587407 / 10000000000, 15702544143 / 10000000000]
l : [-51256263 / 1000000000, 994589849 / 10000000000, -8160841517 / 10000000000]
a : [2542164291 / 5000000000, -5819871877 / 10000000000, 6681980199 / 10000000000]
d : [946461651 / 10000000000, -1392768531 / 2000000000, -2323992903 / 10000000000]
c : [1131189471 / 2500000000, 984715159 / 5000000000, 437227343 / 10000000000]
n : [4473147581 / 5000000000, 20256680681 / 10000000000, 7213010737 / 10000000000]
j : [7207275949 / 10000000000, 11072305301 / 10000000000, 1812344493 / 5000000000]
b : [2164507859 / 2500000000, 1544227959 / 5000000000, 379500809 / 400000000]
k : [1091012831 / 5000000000, 10053772539 / 10000000000, -4960980153 / 10000000000]
i : [10389772957 / 10000000000, 12278528679 / 10000000000, 3256999089 / 2500000000]
f : [6836567953 / 10000000000, 3341877939 / 10000000000, 2571597901 / 2500000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 15
|E| = 39
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 9917594434383669041415550902277858335920682717076756574667 / 256969627396882800291705680267327695829900000000000000000000
Collision distance in [19645463 / 100000000, 2455683 / 12500000] ~ [0.19645, 0.19645]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1331 / 10000, 1333 / 10000] ~ [0.1331, 0.1333]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1367830062568749187212776911997339909 / 5000000000000000000000000000000000000000
rho in [1653983 / 100000000, 51687 / 3125000] ~ [0.01654, 0.01654]
sigma_min ^ 2 / (16 * E ^ .5) in [1771561 / 9991996800, 1776889 / 9991996784] ~ [0.00018, 0.00018]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)