show/hide visualization coordinates
a : (0.3855014037588236, 0.11939654066470579, 0.6977620595823529)
b : (0.7256624064588236, -0.8195986806352942, 0.7485406622823529)
c : (1.2825598276588237, -0.10859023303529419, 0.31920134468235295)
d : (1.0806668315588235, 0.8309685096647058, 0.595730885082353)
e : (0.12198793665882363, 1.0366988339647059, 0.39923709398235296)
f : (-0.5502565269411763, 0.2963979493647058, 0.392757803082353)
g : (-0.21040783374117644, -0.6426599688352941, 0.444459755982353)
h : (0.2737815699588236, -1.4569868703352942, 0.12440926168235295)
i : (0.5518785133588237, -0.5526482157352941, -0.1993710465176471)
j : (0.6420537271588236, 0.4431556877647058, -0.214960029917647)
k : (-0.11962976454117635, 0.9853232759647057, -0.5697734522176472)
l : (-0.8175071740411763, 1.2169738303647057, 0.10794709638235295)
m : (-0.9572197061411765, 0.4424215129647058, -0.5089395350176471)
n : (-1.0538958968411765, -0.4429263786352942, -0.054172754317647065)
o : (-0.3156639349411764, -0.9471828872352941, -0.5022117526176471)
p : (-0.08921737904117644, -0.0008367409352941779, -0.7327566041176472)
q : (-0.9502940003411764, -0.39990616533529416, -1.0478607880176471)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['f', 'l', 'm'], ['k', 'e', 'l'], ['h', 'o', 'i'], ['i', 'j', 'p'], ['i', 'j', 'c'], ['d', 'e', 'a'], ['f', 'e', 'a'], ['l', 'e', 'f'], ['k', 'm', 'l'], ['d', 'e', 'j'], ['j', 'k', 'p'], ['d', 'c', 'a'], ['i', 'o', 'p'], ['b', 'i', 'c'], ['o', 'n', 'g'], ['k', 'm', 'p'], ['b', 'c', 'a'], ['q', 'm', 'n'], ['b', 'g', 'a'], ['q', 'o', 'n'], ['f', 'm', 'n'], ['j', 'd', 'c'], ['q', 'o', 'p'], ['q', 'm', 'p'], ['h', 'o', 'g'], ['b', 'h', 'g'], ['b', 'h', 'i'], ['f', 'n', 'g'], ['j', 'e', 'k'], ['f', 'g', 'a']]
Coordinate Data:
c : [-7304106909 / 10000000000, 5058285481 / 10000000000, 676047807 / 5000000000]
n : [501889073 / 312500000, 8401646937 / 10000000000, 1271459151 / 2500000000]
l : [3424140777 / 2500000000, -8197355153 / 10000000000, 3464638097 / 10000000000]
b : [-1735132697 / 10000000000, 12168369957 / 10000000000, -1470648781 / 5000000000]
e : [4301612001 / 10000000000, -6394605189 / 10000000000, 551738121 / 10000000000]
h : [695918917 / 2500000000, 9271125927 / 5000000000, 825004111 / 2500000000]
i : [1353117 / 5000000000, 2374716327 / 2500000000, 3268909763 / 5000000000]
p : [3206832579 / 5000000000, 24879691 / 62500000, 5935837551 / 5000000000]
o : [8678130717 / 10000000000, 13444212023 / 10000000000, 9566226587 / 10000000000]
d : [-1321294237 / 2500000000, -2168650973 / 5000000000, -141319979 / 1000000000]
f : [11024056637 / 10000000000, 1008403657 / 10000000000, 61653103 / 1000000000]
q : [15024431371 / 10000000000, 1992861201 / 2500000000, 15022716941 / 10000000000]
k : [6717789013 / 10000000000, -5880849609 / 10000000000, 10241843583 / 10000000000]
m : [15093688429 / 10000000000, -451831979 / 10000000000, 9633504411 / 10000000000]
a : [166647733 / 1000000000, 173651109 / 625000000, -486702307 / 2000000000]
j : [-56190369 / 625000000, -459173727 / 10000000000, 83671367 / 125000000]
g : [1525113941 / 2000000000, 10398982839 / 10000000000, 99511501 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 500921749079131761580983197651860427964848040487434551725729 / 999996575874987499657420114465140457024500000000000000000000
Collision distance in [35387973 / 50000000, 70775947 / 100000000] ~ [0.70776, 0.70776]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [6111 / 10000, 6113 / 10000] ~ [0.6111, 0.6113]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 4929280645278968513163 / 5000000000000000000000000000000000000000
rho in [992902879 / 1000000000000000000, 10992902879 / 1000000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [12448107 / 3577708768, 37368769 / 10733126288] ~ [0.00348, 0.00348]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-2499 / 12500000, 20097 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-2499 / 670820393, 20097 / 5366563144] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70775946 / 412310563, 70775947 / 412310562] ~ [0.17166, 0.17166]
Success: LHS < CD / |V| ^ .5
Success: existence proven