show/hide visualization coordinates
a : (-0.32346408695263174, -0.6018688443263158, -0.5957559472894738)
b : (0.3776428687473683, 0.07359882667368417, -0.8242126435894738)
c : (0.6199387258473683, -0.7386702585263158, -0.29363592828947377)
d : (-0.12780385125263172, -1.2120891175263158, 0.1719342835105262)
e : (-0.9390939384526318, -0.6277847200263158, 0.1918532536105262)
f : (-1.2872326494526316, -0.3590946747263158, -0.7062587088894738)
g : (-0.5827695663526317, 0.34747811757368424, -0.7732411970894738)
h : (0.13627893544736835, 1.0424203052736842, -0.7682805929894738)
i : (1.0943339292473684, 0.7616852889736843, -0.7106743491894738)
j : (1.3342305310473683, -0.20830594692631577, -0.7502549310894737)
k : (0.8771652938473684, 0.16110706067368424, 0.058834309310526245)
l : (0.36102080684736826, -0.47270345292631577, 0.6349238002105263)
m : (-0.4670307093526317, -0.8570749453263158, 1.0430772547105263)
n : (-0.5813077927526317, 0.10004487137368417, 0.7768773212105261)
o : (-1.1933693419526317, 0.3236547553736842, 0.018339728210526207)
p : (-0.3008018206526317, 0.7690618009736843, 0.08859485921052623)
q : (0.6318231817473683, 1.1298350737736842, 0.09589216631052622)
r : (0.3299842446473683, 0.5095547633736841, 0.8198711664105262)
s : (0.04045523974736831, -0.1408489037263158, 1.5221161557105263)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['r', 'q', 'p'], ['d', 'a', 'c'], ['d', 'a', 'e'], ['k', 'i', 'q'], ['l', 's', 'r'], ['r', 'n', 'p'], ['l', 'k', 'r'], ['s', 'r', 'n'], ['h', 'p', 'q'], ['n', 'p', 'o'], ['b', 'j', 'i'], ['l', 'k', 'c'], ['b', 'g', 'a'], ['m', 'e', 'n'], ['i', 'h', 'q'], ['e', 'n', 'o'], ['s', 'm', 'n'], ['k', 'r', 'q'], ['b', 'a', 'c'], ['j', 'k', 'i'], ['l', 'd', 'c'], ['d', 'e', 'm'], ['g', 'p', 'o'], ['f', 'e', 'o'], ['d', 'm', 'l'], ['b', 'j', 'c'], ['o', 'g', 'f'], ['b', 'g', 'h'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['g', 'h', 'p'], ['l', 's', 'm'], ['g', 'a', 'f']]
Coordinate Data:
d : [106698353 / 250000000, -7127650623 / 10000000000, 7909628499 / 10000000000]
c : [11745359891 / 10000000000, -2393462033 / 10000000000, 3253926381 / 10000000000]
n : [-53421059 / 2000000000, 2996844633 / 5000000000, 3489764719 / 2500000000]
s : [595052503 / 1000000000, 716950303 / 2000000000, 21411447221 / 10000000000]
q : [237284089 / 200000000, 1629159129 / 1000000000, 7149207327 / 10000000000]
p : [1268977213 / 5000000000, 6341929281 / 5000000000, 442264641 / 625000000]
i : [659572477 / 400000000, 6305046721 / 5000000000, -229114457 / 2500000000]
m : [875665539 / 10000000000, -3577508901 / 10000000000, 16621058211 / 10000000000]
a : [2311331763 / 10000000000, -1025447891 / 10000000000, 232726191 / 10000000000]
b : [233060033 / 250000000, 5729228819 / 10000000000, -512960193 / 2500000000]
r : [8845815079 / 10000000000, 5044394093 / 5000000000, 899312333 / 625000000]
e : [-120155211 / 312500000, -160575831 / 1250000000, 40544091 / 50000000]
j : [18888277943 / 10000000000, 2910181083 / 10000000000, -1312263647 / 10000000000]
k : [14317625571 / 10000000000, 6604311159 / 10000000000, 6778628757 / 10000000000]
l : [9156180701 / 10000000000, 266206023 / 10000000000, 6269761833 / 5000000000]
h : [6908761987 / 10000000000, 3083488721 / 2000000000, -746260133 / 5000000000]
f : [-3663176931 / 5000000000, 280458761 / 2000000000, -34892057 / 400000000]
g : [-281723031 / 10000000000, 264625679 / 312500000, -1542126307 / 10000000000]
o : [-6387720787 / 10000000000, 4114894053 / 5000000000, 3186841473 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 496969432440253217818648553567766747764482352943155306041 / 976229133457864276375304174421203380390625000000000000000
Collision distance in [2853967 / 4000000, 8918647 / 12500000] ~ [0.71349, 0.71349]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [4499 / 10000, 4501 / 10000] ~ [0.4499, 0.4501]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 9275431208548461962127 / 5000000000000000000000000000000000000000
rho in [2724031 / 2000000000000000, 22724031 / 2000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [20241001 / 11426285488, 2894143 / 1632326496] ~ [0.00177, 0.00177]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19983 / 100000000, 4029 / 20000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-6661 / 1904380912, 6715 / 1904380912] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [14269835 / 87177979, 35674588 / 217944947] ~ [0.16369, 0.16369]
Success: LHS < CD / |V| ^ .5
Success: existence proven