show/hide visualization coordinates
a : (0.14191358164615375, 1.019626102376923, 0.7734648111692308)
b : (0.6747808514461536, 0.18855819027692305, 0.6141581939692309)
c : (0.42395163014615367, 0.7767450611769231, -0.15468568263076918)
d : (-0.5384452819538463, 0.7107934960769231, 0.10883390766923084)
e : (-0.28761606065384626, 0.12260662507692305, 0.8776777842692309)
f : (0.18793647394615376, -0.679433600123077, 0.5163174879692308)
g : (0.5358205749461536, -0.20721844372307693, -0.29361429813076917)
h : (-0.2200133512538463, 0.2771962927769231, -0.7341338085307691)
i : (-0.27164448175384626, 1.274003211376923, -0.6732224517307692)
j : (-0.5793641720538463, -0.28364032182307697, 0.01174103276923083)
k : (-0.4316868618538463, -1.2726311386230769, 0.0023295484692308355)
l : (0.5307100503461536, -1.2066795735230769, -0.26119004183076916)
m : (-0.16634295295384632, -0.719925901323077, -0.7876764834307692)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['m', 'g', 'l'], ['c', 'a', 'd'], ['a', 'b', 'e'], ['j', 'f', 'e'], ['m', 'k', 'l'], ['j', 'f', 'k'], ['h', 'd', 'i'], ['m', 'h', 'j'], ['c', 'g', 'b'], ['f', 'b', 'e'], ['f', 'g', 'l'], ['h', 'j', 'd'], ['c', 'h', 'i'], ['k', 'f', 'l'], ['m', 'j', 'k'], ['j', 'd', 'e'], ['c', 'd', 'i'], ['a', 'd', 'e'], ['c', 'a', 'b'], ['c', 'h', 'g'], ['f', 'g', 'b'], ['m', 'h', 'g']]
Coordinate Data:
g : [10558627847 / 10000000000, 200737311 / 1000000000, 33297259 / 625000000]
i : [7762429 / 31250000, 16819589661 / 10000000000, -203957837 / 625000000]
m : [442124071 / 1250000000, -1559850733 / 5000000000, -4407865709 / 10000000000]
f : [7079786837 / 10000000000, -1357389227 / 5000000000, 1726414801 / 2000000000]
c : [9439938399 / 10000000000, 11847008159 / 10000000000, 1922042299 / 10000000000]
e : [2324261491 / 10000000000, 2652811899 / 5000000000, 1530709621 / 1250000000]
l : [10507522601 / 10000000000, -1996809547 / 2500000000, 856998707 / 10000000000]
j : [-593219623 / 10000000000, 1243154329 / 10000000000, 3586309453 / 10000000000]
a : [3309778957 / 5000000000, 14275818571 / 10000000000, 11203547237 / 10000000000]
d : [-92015361 / 5000000000, 2796873127 / 2500000000, 2278619101 / 5000000000]
b : [2987057653 / 2500000000, 119302789 / 200000000, 1922096213 / 2000000000]
k : [883553479 / 10000000000, -8646753839 / 10000000000, 349219461 / 1000000000]
h : [600057717 / 2000000000, 274060819 / 400000000, -48405487 / 125000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 13
|E| = 33
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 499999999719815482793120309557920320725680983378845317798241 / 999999999823386480960058402511781345276600000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [203 / 250, 4061 / 5000] ~ [0.812, 0.8122]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 3364471192140668295899 / 2500000000000000000000000000000000000000
rho in [116008123 / 100000000000000000, 1116008123 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [824180 / 114891253, 16491721 / 2297825056] ~ [0.00717, 0.00718]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9997 / 50000000, 627 / 3125000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [71807033 / 1562500, 114891253 / 2500000] ~ [45.9565, 45.9565]
LHS := (LHS NUM) / (LHS DEN) in [-9997 / 2297825056, 627 / 143614066] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [35355339 / 180277564, 70710679 / 360555127] ~ [0.19612, 0.19612]
Success: LHS < CD / |V| ^ .5
Success: existence proven