show/hide visualization coordinates
a : (0.26112946819444455, 1.1359159774611112, -0.7083406575833333)
b : (0.5867166137944446, 0.20438547776111116, -0.8703404686833333)
c : (-0.36113591790555544, 0.4459913846611112, -1.0781917704833333)
d : (-0.24962339170555548, 1.3218361085611112, -1.5477244915833333)
e : (-0.7273650443055555, 1.2822630449611112, -0.6701158739833333)
f : (-0.20517147980555547, 1.171977760961111, 0.17555015791666673)
g : (0.5936851100944445, 0.5825868277611111, 0.05535666261666672)
h : (0.7604465240944445, -0.39301516173888884, -0.08744175658333325)
i : (-0.16303062770555546, -0.31757787703888885, -0.4636055053833332)
j : (-0.7690923624055555, 0.4198908720611112, -0.16556353188333328)
k : (-0.17109939300555546, 0.27850262796111114, 0.6233685139166667)
l : (0.7598837430944445, -0.016186896038888843, 0.8388412139166668)
m : (0.9204335271944444, -0.9928954872388889, 0.6964892055166667)
n : (0.04436077459444454, -1.0220105275388889, 0.2151900811166667)
o : (-0.7745848016055554, -0.45692618673888885, 0.3152292274166667)
p : (0.00109426379444455, -0.6634449517388888, 0.9116116442166668)
q : (0.21281187599444457, -1.6380397428388889, 0.9846913695166668)
r : (-0.7194588824055554, -1.3432532512388888, 0.7749959800166668)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['l', 'g', 'h'], ['c', 'i', 'b'], ['n', 'i', 'o'], ['e', 'a', 'f'], ['a', 'f', 'g'], ['q', 'p', 'm'], ['l', 'k', 'g'], ['q', 'p', 'r'], ['c', 'e', 'd'], ['c', 'a', 'd'], ['h', 'm', 'l'], ['k', 'f', 'g'], ['h', 'n', 'i'], ['p', 'k', 'o'], ['h', 'i', 'b'], ['p', 'r', 'o'], ['e', 'a', 'd'], ['l', 'p', 'm'], ['j', 'k', 'f'], ['j', 'i', 'o'], ['c', 'j', 'e'], ['c', 'j', 'i'], ['h', 'g', 'b'], ['q', 'n', 'm'], ['q', 'n', 'r'], ['k', 'j', 'o'], ['l', 'p', 'k'], ['n', 'r', 'o'], ['a', 'g', 'b'], ['e', 'j', 'f'], ['h', 'n', 'm'], ['c', 'a', 'b']]
Coordinate Data:
l : [5657625357 / 5000000000, 749320149 / 2000000000, 1712184367 / 1250000000]
k : [2005419353 / 10000000000, 1338699197 / 2000000000, 360710873 / 312500000]
c : [13131763 / 1250000000, 130755993 / 156250000, -1368213727 / 2500000000]
i : [1043053503 / 5000000000, 146538187 / 2000000000, 673007743 / 10000000000]
n : [4160021029 / 10000000000, -631163557 / 1000000000, 932620451 / 1250000000]
a : [1265541593 / 2000000000, 381690737 / 250000000, -1774343779 / 10000000000]
f : [332939697 / 2000000000, 3125649463 / 2000000000, 883070547 / 1250000000]
r : [-3478175541 / 10000000000, -9524062807 / 10000000000, 13059022597 / 10000000000]
b : [9583579421 / 10000000000, 5952324483 / 10000000000, -339434189 / 1000000000]
e : [-88930929 / 250000000, 3346220031 / 2000000000, -1392095943 / 10000000000]
d : [610089683 / 5000000000, 17126830791 / 10000000000, -10168182119 / 10000000000]
q : [5844532043 / 10000000000, -12471927723 / 10000000000, 3788994123 / 2500000000]
o : [-4029434733 / 10000000000, -330396081 / 5000000000, 8461355071 / 10000000000]
m : [2584149711 / 2000000000, -6020485167 / 10000000000, 3068488713 / 2500000000]
j : [-3974510341 / 10000000000, 4053689213 / 5000000000, 1826713739 / 5000000000]
g : [9427016 / 9765625, 9734337983 / 10000000000, 5862629423 / 10000000000]
p : [3727355921 / 10000000000, -681494953 / 2500000000, 14425179239 / 10000000000]
h : [2830219631 / 2500000000, -2710239 / 1250000000, 4434645231 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 18
|E| = 48
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 5732660692202362793592077162996136698207457212751287034889 / 15047331573906996121373476138141717192270312500000000000000
Collision distance in [61723191 / 100000000, 7715399 / 12500000] ~ [0.61723, 0.61723]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2107 / 5000, 527 / 1250] ~ [0.4214, 0.4216]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 102585942810358798359001 / 10000000000000000000000000000000000000000
rho in [320290403 / 100000000000000000, 1320290403 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [634207 / 395897328, 1110916 / 692820323] ~ [0.0016, 0.0016]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9979 / 50000000, 10087 / 50000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [692820323 / 12500000, 173205081 / 3125000] ~ [55.42563, 55.42563]
LHS := (LHS NUM) / (LHS DEN) in [-9979 / 2771281292, 10087 / 2771281292] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [61723191 / 424264069, 15430798 / 106066017] ~ [0.14548, 0.14548]
Success: LHS < CD / |V| ^ .5
Success: existence proven