show/hide visualization coordinates
a : (-0.002248600674999879, -0.05330142098750007, -0.008103462262500027)
b : (0.9929747956250001, -0.007663418387500065, -0.10856047676250002)
c : (0.5874364529250001, -0.15833565848750003, 0.7927274047375)
d : (-0.40632142787500003, -0.1424689126875, 0.9010734340375)
e : (-0.987540256375, 0.08026661031249993, 0.11921059073750001)
f : (-0.590309832275, 0.11637991621249993, -0.7973545607624999)
g : (0.40338337262500007, 0.11790323971249994, -0.9062481164625)
h : (0.0026254960250000625, 0.047219644312499975, 0.00725518673750003)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'c', 'b'], ['a', 'g', 'b'], ['f', 'h', 'e'], ['g', 'h', 'b'], ['h', 'e', 'd'], ['f', 'a', 'e'], ['a', 'e', 'd'], ['h', 'c', 'd'], ['f', 'g', 'h'], ['a', 'c', 'd'], ['a', 'c', 'b'], ['f', 'a', 'g']]
Coordinate Data:
b : [-3775181533 / 10000000000, 4449263251 / 10000000000, 766067197 / 1250000000]
e : [16029968987 / 10000000000, 892490741 / 2500000000, 3850826901 / 10000000000]
g : [2120732697 / 10000000000, 319359667 / 1000000000, 14105413973 / 10000000000]
d : [5108890351 / 5000000000, 2898659097 / 5000000000, -991950383 / 2500000000]
h : [6128311463 / 10000000000, 243777039 / 625000000, 4970380941 / 10000000000]
c : [140100947 / 5000000000, 1488996413 / 2500000000, -2884341239 / 10000000000]
a : [617705243 / 1000000000, 4905643277 / 10000000000, 5123967431 / 10000000000]
f : [6028832373 / 5000000000, 641765981 / 2000000000, 813529901 / 625000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 8
|E| = 18
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 4804404675487464264364428944057195809781323696928462689 / 479703101776682025049728177565280992591625000000000000000
Collision distance in [5003841 / 50000000, 10007683 / 100000000] ~ [0.10008, 0.10008]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [353 / 2500, 707 / 5000] ~ [0.1412, 0.1414]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 135212475171854233566050053423851143 / 1250000000000000000000000000000000000000
rho in [1040047 / 100000000, 65003 / 6250000] ~ [0.0104, 0.0104]
sigma_min ^ 2 / (16 * E ^ .5) in [124609 / 424264069, 499849 / 1697056272] ~ [0.00029, 0.00029]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)