show/hide visualization coordinates
a : (0.36162313987647066, 0.3668574507352941, -0.34140885212352934)
b : (1.1088594459764707, -0.2792757325647059, -0.18468588542352937)
c : (0.41392192787647064, -0.4773358833647059, -0.8752748064235294)
d : (-0.3512398459235294, 0.15207185343529417, -1.0093411351235293)
e : (-0.4212545795235294, 0.9793578715352941, -0.4527947005235294)
f : (0.2738613469764706, 1.177469188335294, 0.23797258227647067)
g : (1.0388218324764706, 0.5482173983352941, 0.3719957989764706)
h : (0.8822130959764707, -0.3479452353647059, 0.7866399727764706)
i : (0.1963521546764706, -0.5776902093647058, 0.09579171817647059)
j : (-0.5078682406235294, -0.7441086345647059, -0.5947399158235294)
k : (-0.28123340232352934, -0.6755568027647059, -1.5662772744235294)
l : (-0.6102561055235294, 0.08558524603529416, -0.045544723323529324)
m : (-0.6479259041235294, 0.9106988805352941, 0.5185283011764705)
n : (0.12255506357647061, 0.2943482371352941, 0.6825040489764707)
o : (-0.03939509022352938, -0.6146608383647059, 1.0671521050764707)
p : (-0.7345015192235294, -0.8127590668647059, 0.37640233467647066)
q : (-0.8045333199235294, 0.014726277135294175, 0.9330804310764707)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['p', 'o', 'i'], ['e', 'm', 'f'], ['i', 'c', 'j'], ['a', 'e', 'd'], ['l', 'e', 'm'], ['q', 'p', 'l'], ['g', 'f', 'n'], ['q', 'p', 'o'], ['l', 'j', 'd'], ['n', 'h', 'g'], ['l', 'e', 'd'], ['o', 'i', 'h'], ['q', 'o', 'n'], ['o', 'h', 'n'], ['q', 'm', 'n'], ['p', 'i', 'j'], ['a', 'f', 'g'], ['a', 'c', 'd'], ['b', 'a', 'g'], ['c', 'd', 'k'], ['a', 'e', 'f'], ['b', 'h', 'g'], ['j', 'd', 'k'], ['b', 'i', 'h'], ['f', 'm', 'n'], ['b', 'a', 'c'], ['c', 'j', 'k'], ['q', 'l', 'm'], ['b', 'i', 'c'], ['p', 'l', 'j']]
Coordinate Data:
q : [-608281249 / 2000000000, 5612486129 / 10000000000, 14985373571 / 10000000000]
p : [-1170544119 / 5000000000, -2662367311 / 10000000000, 9418592607 / 10000000000]
n : [622947759 / 1000000000, 8408705729 / 10000000000, 49918439 / 40000000]
h : [6913028957 / 5000000000, 496442751 / 2500000000, 3380242247 / 2500000000]
i : [6967448501 / 10000000000, -19479921 / 625000000, 3306243221 / 5000000000]
f : [967817553 / 1250000000, 17239915241 / 10000000000, 8034295083 / 10000000000]
j : [-18688863 / 2500000000, -493965747 / 2500000000, -146414949 / 5000000000]
e : [791381159 / 10000000000, 15258802073 / 10000000000, 225324451 / 2000000000]
d : [298305699 / 2000000000, 1746485473 / 2500000000, -4438842091 / 10000000000]
k : [2191592931 / 10000000000, -129034467 / 1000000000, -2502050871 / 2500000000]
l : [-1098634101 / 10000000000, 3160537909 / 5000000000, 5199122027 / 10000000000]
a : [8620158353 / 10000000000, 1826759573 / 2000000000, 2240480739 / 10000000000]
g : [15392145279 / 10000000000, 10947397341 / 10000000000, 37498109 / 40000000]
o : [1152494013 / 2500000000, -340692513 / 5000000000, 16326090311 / 10000000000]
m : [-1475332087 / 10000000000, 14572212163 / 10000000000, 677490767 / 625000000]
b : [8046260707 / 5000000000, 167029127 / 625000000, 1903855203 / 5000000000]
c : [9143146233 / 10000000000, 172966131 / 2500000000, -774544701 / 2500000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 555206531156341383638523673509730317051258505696079119641 / 1110680641280033461392307130140241016341000000000000000000
Collision distance in [70702159 / 100000000, 883777 / 1250000] ~ [0.70702, 0.70702]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [259 / 2500, 519 / 5000] ~ [0.1036, 0.1038]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 58417140704864339016939153716449081 / 5000000000000000000000000000000000000000
rho in [34181 / 10000000, 341811 / 100000000] ~ [0.00342, 0.00342]
sigma_min ^ 2 / (16 * E ^ .5) in [67081 / 670820394, 269361 / 2683281572] ~ [0.0001, 0.0001]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)