show/hide visualization coordinates
a : (-0.02007787683529405, -0.8762208540823531, 0.3092836647941177)
b : (-0.469790267935294, -0.16909931928235306, -0.2363699801058823)
c : (0.40243615866470595, -0.5541752736823531, -0.5379285481058823)
d : (0.7926339752647059, -0.29468033258235304, 0.3454785150941177)
e : (0.12480913626470602, -0.26746523708235304, 1.0892992749941177)
f : (-0.402148035735294, -1.109656525382353, 1.2034481803941177)
g : (-0.7118599213352941, -0.2869836879823531, 0.7267009198941177)
h : (-0.820211173335294, 0.605870398317647, 0.2895835594941177)
i : (-0.18761258513529405, 0.761612188717647, -0.4690754684058823)
j : (-0.12345365503529404, 0.03413508401764698, -1.1522011478058822)
k : (0.863559787564706, -0.06524360418235303, -1.2784086771058822)
l : (0.7327650811647061, 0.37830278961764696, -0.3917524072058823)
m : (0.16245747326470594, 0.477828805817647, 0.4236271390941177)
n : (-0.445617909335294, 0.544250165917647, 1.2147229183941177)
o : (-0.6470738624352941, -0.292083530182353, 1.7245870647941177)
p : (0.45484653086470594, 0.846172248217647, -1.2307157251058822)
q : (0.294337144064706, 0.26743668381764696, -2.0302792831058825)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['d', 'l', 'c'], ['n', 'g', 'o'], ['b', 'j', 'c'], ['g', 'f', 'o'], ['k', 'q', 'j'], ['n', 'e', 'm'], ['i', 'p', 'j'], ['n', 'o', 'e'], ['i', 'b', 'h'], ['d', 'l', 'm'], ['d', 'e', 'm'], ['q', 'p', 'j'], ['n', 'h', 'm'], ['d', 'c', 'a'], ['i', 'l', 'm'], ['b', 'g', 'a'], ['g', 'f', 'a'], ['d', 'e', 'a'], ['b', 'g', 'h'], ['p', 'k', 'q'], ['f', 'o', 'e'], ['k', 'l', 'p'], ['f', 'e', 'a'], ['i', 'b', 'j'], ['i', 'l', 'p'], ['n', 'g', 'h'], ['k', 'l', 'c'], ['c', 'b', 'a'], ['i', 'h', 'm'], ['k', 'j', 'c']]
Coordinate Data:
a : [1101142589 / 2000000000, -4510025757 / 10000000000, 5686971 / 8000000]
g : [-564843 / 4000000, 86396619 / 625000000, 11282886301 / 10000000000]
q : [4324931577 / 5000000000, 3463274811 / 5000000000, -16286915729 / 10000000000]
i : [1915182931 / 5000000000, 11868304671 / 10000000000, -337438791 / 5000000000]
m : [3665533223 / 5000000000, 4515235421 / 5000000000, 8252148493 / 10000000000]
c : [97308533 / 100000000, -1289569953 / 10000000000, -1363408379 / 10000000000]
j : [4471955163 / 10000000000, 574191703 / 1250000000, -938266797 / 1250000000]
o : [-764246911 / 10000000000, 665673741 / 5000000000, 85046991 / 40000000]
k : [14342089589 / 10000000000, 1799873371 / 5000000000, -8768209669 / 10000000000]
p : [5127478511 / 5000000000, 6356952633 / 5000000000, -8291280149 / 10000000000]
h : [-124781001 / 500000000, 10310886767 / 10000000000, 6911712697 / 10000000000]
n : [62515631 / 500000000, 9694684443 / 10000000000, 8081553143 / 5000000000]
d : [6816415733 / 5000000000, 652689729 / 5000000000, 7470662253 / 10000000000]
b : [504294517 / 5000000000, 2561189591 / 10000000000, 1652177301 / 10000000000]
e : [1738645769 / 2500000000, 1577530413 / 10000000000, 3727217463 / 2500000000]
l : [521365701 / 400000000, 200880267 / 250000000, 9835303 / 1000000000]
f : [421252839 / 2500000000, -684438247 / 1000000000, 8025179453 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 1100834459872494689714604456285635208574376393649368361 / 2424153766344535910861521439486039125846679687500000000
Collision distance in [13477549 / 20000000, 33693873 / 50000000] ~ [0.67388, 0.67388]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2851 / 5000, 713 / 1250] ~ [0.5702, 0.5704]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 113603477545958359777 / 100000000000000000000000000000000000000
rho in [26646233 / 25000000000000000, 276646233 / 25000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [8128201 / 2683281576, 2033476 / 670820393] ~ [0.00303, 0.00303]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-1999 / 10000000, 4021 / 20000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-9995 / 2683281572, 20105 / 5366563144] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [67387745 / 412310563, 11231291 / 68718427] ~ [0.16344, 0.16344]
Success: LHS < CD / |V| ^ .5
Success: existence proven