show/hide visualization coordinates
a : (0.4818873065058824, -0.5270129082294117, 0.5542449250000001)
b : (-0.33426251139411767, -0.8368247269294118, 0.06647847250000005)
c : (0.5481379476058823, -1.2741112800294117, -0.10715879159999997)
d : (1.2009609950058824, -0.5173403049294117, -0.14062158849999995)
e : (1.2513343512058823, 0.1059490902705883, 0.6397455399)
f : (0.31349604910588236, 0.4509002150705883, 0.6780605432)
g : (-0.42199238109411763, -0.20735802722941174, 0.8385375007)
h : (-1.1282609419941176, -0.23234229402941176, 0.1310344928)
i : (-0.6762195453941177, -0.37163922052941173, -0.7500188213)
j : (0.30790288910588237, -0.42714360742941176, -0.5814296834)
k : (0.7527239404058823, 0.3755164522705883, -0.18409977019999996)
l : (1.0663271229058824, 1.0722939912705884, 0.4610003026)
m : (0.18386544950588235, 1.1765468901705884, 0.0023144298000000174)
n : (-0.5866882797941176, 0.5971074516705882, 0.26782693030000004)
o : (-1.1412345438941176, 0.49252827067058824, -0.5577284198)
p : (-1.6744851502941176, -0.34147078012941173, -0.6994654093999999)
q : (-0.14349269749411764, 0.46440078807058827, -0.6187206526)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'o', 'q'], ['i', 'j', 'q'], ['f', 'l', 'm'], ['k', 'e', 'l'], ['d', 'e', 'a'], ['f', 'e', 'a'], ['l', 'e', 'f'], ['k', 'm', 'l'], ['h', 'i', 'p'], ['b', 'j', 'c'], ['h', 'o', 'p'], ['d', 'c', 'a'], ['b', 'j', 'i'], ['i', 'o', 'p'], ['k', 'm', 'q'], ['d', 'e', 'k'], ['h', 'o', 'n'], ['b', 'c', 'a'], ['q', 'm', 'n'], ['b', 'g', 'a'], ['q', 'o', 'n'], ['f', 'm', 'n'], ['j', 'd', 'c'], ['h', 'n', 'g'], ['j', 'k', 'q'], ['b', 'h', 'g'], ['b', 'h', 'i'], ['f', 'n', 'g'], ['d', 'k', 'j'], ['f', 'g', 'a']]
Coordinate Data:
k : [2660468543 / 2000000000, 1548452613 / 2000000000, 732315179 / 2500000000]
c : [11256482787 / 10000000000, -4377007129 / 5000000000, 1849335251 / 5000000000]
n : [-91779487 / 10000000000, 9958173059 / 10000000000, 7448527721 / 10000000000]
l : [821918727 / 500000000, 2942007691 / 2000000000, 2345065361 / 2500000000]
b : [2432478197 / 10000000000, -4381148727 / 10000000000, 5435043143 / 10000000000]
e : [18288446823 / 10000000000, 1009317889 / 2000000000, 11167713817 / 10000000000]
d : [17784713261 / 10000000000, -1186304507 / 10000000000, 3364042533 / 10000000000]
h : [-5507506109 / 10000000000, 831837801 / 5000000000, 3040301673 / 5000000000]
p : [-342804631 / 312500000, 572390741 / 10000000000, -556098919 / 2500000000]
o : [-352327633 / 625000000, 8912381249 / 10000000000, -40351289 / 500000000]
f : [4455031901 / 5000000000, 8496100693 / 10000000000, 231017277 / 200000000]
q : [271261021 / 625000000, 8631106423 / 10000000000, -354237027 / 2500000000]
i : [-987092143 / 10000000000, 270706337 / 10000000000, -545985959 / 2000000000]
m : [3806878903 / 5000000000, 3938141861 / 2500000000, 1198350679 / 2500000000]
a : [1324247047 / 1250000000, -64151527 / 500000000, 2578176917 / 2500000000]
j : [4427066101 / 5000000000, -71084383 / 2500000000, -65252401 / 625000000]
g : [3110359 / 20000000, 191351827 / 1000000000, 526225337 / 400000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 121159466539966460919713217647633099907983073966820217592841 / 249789200098871222708014932322342037707400000000000000000000
Collision distance in [13929061 / 20000000, 34822653 / 50000000] ~ [0.69645, 0.69645]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2783 / 5000, 348 / 625] ~ [0.5566, 0.5568]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 376601919287335398281711 / 10000000000000000000000000000000000000000
rho in [613679003 / 100000000000000000, 1613679003 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [7745089 / 2683281576, 1937664 / 670820393] ~ [0.00289, 0.00289]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19941 / 100000000, 5039 / 25000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-19941 / 5366563144, 5039 / 1341640786] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [69645305 / 412310563, 11607551 / 68718427] ~ [0.16891, 0.16891]
Success: LHS < CD / |V| ^ .5
Success: existence proven