show/hide visualization coordinates
a : (1.428970780982353, 0.8419906035470588, -0.0976433954764706)
b : (0.43834131398235304, 0.9684806323470587, -0.15024866407647053)
c : (1.008330256482353, 1.6618940059470588, 0.29063048682352943)
d : (1.931685587582353, 1.706439835247059, -0.09074379617647055)
e : (1.767537070982353, 1.2167329412470589, 0.7655063306235295)
f : (0.871675419182353, 0.7739896072470588, 0.7298253151235294)
g : (0.8175139869823531, 0.06113517014705877, 0.03058510682352944)
h : (-0.041789021917646996, 0.1525481126470588, -0.47278253817647053)
i : (-0.010490056417646998, 0.3606263375470588, 0.5047822987235294)
j : (0.07217290578235303, -0.5855918589529412, 0.19208628372352943)
k : (-0.5057888320176469, -0.7224020576529413, -0.6124351265764705)
l : (-0.8042256626176469, -0.10942815315294119, 0.11897381862352946)
m : (-0.783024022317647, -1.0973912550529412, 0.27224504832352947)
n : (-1.0332961462176469, -1.5710527632529414, -0.5721166068764705)
o : (-1.4676096359176471, -0.7009236534529413, -0.3393836375764706)
p : (-1.6833849993176468, -1.5238183385529414, 0.18632347132352944)
q : (-2.006618945217647, -1.4332291658529412, -0.7556043951764706)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['o', 'm', 'p'], ['f', 'e', 'c'], ['d', 'e', 'a'], ['l', 'o', 'm'], ['h', 'k', 'l'], ['f', 'e', 'a'], ['f', 'i', 'g'], ['d', 'c', 'a'], ['k', 'o', 'l'], ['b', 'f', 'c'], ['j', 'h', 'g'], ['i', 'j', 'g'], ['m', 'n', 'p'], ['i', 'l', 'j'], ['d', 'e', 'c'], ['k', 'o', 'n'], ['b', 'c', 'a'], ['b', 'g', 'a'], ['q', 'o', 'n'], ['h', 'k', 'j'], ['j', 'l', 'm'], ['q', 'o', 'p'], ['j', 'm', 'k'], ['b', 'f', 'i'], ['b', 'h', 'g'], ['q', 'n', 'p'], ['k', 'm', 'n'], ['b', 'h', 'i'], ['h', 'l', 'i'], ['f', 'g', 'a']]
Coordinate Data:
c : [-2369030247 / 5000000000, -5900228289 / 5000000000, 545040061 / 2500000000]
n : [15678203533 / 10000000000, 10264505557 / 5000000000, 10807631181 / 10000000000]
l : [13387498697 / 10000000000, 5912765013 / 10000000000, 1948363463 / 5000000000]
b : [961828931 / 10000000000, -2433161421 / 5000000000, 6588951753 / 10000000000]
e : [-12330128639 / 10000000000, -7348845931 / 10000000000, -1284299097 / 5000000000]
d : [-2794322761 / 2000000000, -12245914871 / 10000000000, 2996951537 / 5000000000]
h : [576313229 / 1000000000, 658600471 / 2000000000, 4907145247 / 5000000000]
i : [1090028527 / 2000000000, 606110053 / 5000000000, 309137 / 80000000]
o : [2002133843 / 1000000000, 739232501 / 625000000, 530018843 / 625000000]
j : [4623513013 / 10000000000, 10674402071 / 10000000000, 126624091 / 400000000]
f : [-3371512121 / 10000000000, -2921412591 / 10000000000, -2211788039 / 10000000000]
q : [25411431523 / 10000000000, 957538757 / 500000000, 1580313633 / 1250000000]
k : [10403130391 / 10000000000, 6021252029 / 5000000000, 5605408189 / 5000000000]
m : [6587741147 / 5000000000, 61689047 / 39062500, 2364014629 / 10000000000]
a : [-8944465739 / 10000000000, -1800711277 / 5000000000, 6062899067 / 10000000000]
p : [693096627 / 312500000, 20056666867 / 10000000000, 3223230399 / 10000000000]
g : [-2829897799 / 10000000000, 210356589 / 500000000, 1195153511 / 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 = 55549924782626933862940200604875472258796461681618238658481 / 111142996330204087094448860986751469956500000000000000000000
Collision distance in [70696951 / 100000000, 8837119 / 12500000] ~ [0.70697, 0.70697]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1757 / 5000, 879 / 2500] ~ [0.3514, 0.3516]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 8188913720902549641510634882559219 / 10000000000000000000000000000000000000000
rho in [22623 / 25000000, 90493 / 100000000] ~ [0.0009, 0.0009]
sigma_min ^ 2 / (16 * E ^ .5) in [3087049 / 2683281576, 772641 / 670820393] ~ [0.00115, 0.00115]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [18862299 / 100000000, 4731469 / 25000000] ~ [0.18862, 0.18926]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [6287433 / 1788854384, 4731469 / 1341640786] ~ [0.00351, 0.00353]
CD / |V| ^ .5 in [70696951 / 412310563, 35348476 / 206155281] ~ [0.17147, 0.17147]
Success: LHS < CD / |V| ^ .5
Success: existence proven