show/hide visualization coordinates
a : (0.7397395384350001, -0.8403694029900001, -1.46225242058)
b : (0.08099110633500006, -1.17705419209, -0.78944046358)
c : (-0.24114016676499994, -0.7647691037900001, -1.64163197348)
d : (0.32949251983500005, -1.3476102182900003, -2.22014788728)
e : (0.415836963235, -0.35275314279000014, -2.27300853798)
f : (0.28012734843500003, 0.04233502470999989, -1.3644547732799999)
g : (0.6767562031350001, -0.40630348829000007, -0.5635618291800001)
h : (-0.03939831056499998, -0.6885620172900001, 0.07475448761999998)
i : (-0.43480487036499993, -0.3206303599900001, -0.7668340322800001)
j : (0.14371248693500005, 0.4326481131099999, -0.45397031978)
k : (0.607537810635, 0.02842768860999989, 0.33436618481999997)
l : (-0.15894492536499993, -0.19536161889000014, 0.93638751722)
m : (-0.622314243165, 0.12322931850999991, 0.10946937011999996)
n : (0.006559293935000043, 0.81800073171, 0.45849994782)
o : (0.5327414129350001, 0.4637514317099999, 1.23155704562)
p : (-0.277547335465, 0.3030710114099999, 1.79514560802)
q : (-0.804303132565, 0.5668220456099999, 0.9870700970199999)
r : (-0.13141528526499996, 1.1978204952099998, 1.37319197412)
s : (-0.12246223826499997, 1.10718476561, 2.36903329362)
t : (-0.981164176065, 1.01012291821, 1.86582671142)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'i', 'b'], ['h', 'm', 'l'], ['n', 'j', 'k'], ['n', 'r', 'o'], ['m', 'i', 'j'], ['c', 'f', 'e'], ['m', 'j', 'n'], ['t', 's', 'p'], ['f', 'e', 'a'], ['j', 'k', 'g'], ['l', 'q', 'p'], ['r', 'p', 'o'], ['r', 's', 'p'], ['e', 'd', 'a'], ['c', 'b', 'a'], ['f', 'c', 'i'], ['f', 'j', 'g'], ['c', 'e', 'd'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['o', 'l', 'k'], ['h', 'l', 'k'], ['h', 'm', 'i'], ['q', 't', 'r'], ['g', 'f', 'a'], ['n', 'r', 'q'], ['t', 'q', 'p'], ['h', 'k', 'g'], ['l', 'p', 'o'], ['h', 'g', 'b'], ['c', 'i', 'b'], ['o', 'n', 'k'], ['m', 'q', 'n'], ['i', 'f', 'j'], ['t', 'r', 's'], ['l', 'q', 'm']]
Coordinate Data:
k : [-152647077 / 625000000, 174579451 / 400000000, 25653257 / 156250000]
t : [2688933327 / 2000000000, -5452466021 / 10000000000, -6836398409 / 5000000000]
e : [-262672379 / 5000000000, 8176294589 / 10000000000, 6928888919 / 2500000000]
s : [4857647257 / 10000000000, -1284616899 / 2000000000, -233810783 / 125000000]
g : [-3134537157 / 10000000000, 2177949511 / 2500000000, 2655272147 / 2500000000]
q : [58380281 / 50000000, -203891459 / 2000000000, -2442615337 / 5000000000]
h : [201350399 / 500000000, 5767191667 / 5000000000, 211896271 / 500000000]
c : [3022213271 / 5000000000, 12296454199 / 10000000000, 21401790031 / 10000000000]
l : [326404633 / 625000000, 132047587 / 200000000, -1094601219 / 2500000000]
p : [6408498229 / 10000000000, 1618053047 / 10000000000, -1620748223 / 1250000000]
j : [439180001 / 2000000000, 32228203 / 1000000000, 4762586747 / 5000000000]
i : [3990536789 / 5000000000, 7855066761 / 10000000000, 12653810619 / 10000000000]
a : [-376437051 / 1000000000, 13052457191 / 10000000000, 9803997251 / 5000000000]
b : [2823113811 / 10000000000, 8209652541 / 5000000000, 3219968733 / 2500000000]
f : [83175139 / 1000000000, 2112706457 / 5000000000, 18630018029 / 10000000000]
m : [4928083653 / 5000000000, 427058747 / 1250000000, 778155319 / 2000000000]
d : [84524919 / 2500000000, 283201021 / 156250000, 27186949169 / 10000000000]
o : [-338877851 / 2000000000, 2812211 / 2500000000, -22906563 / 31250000]
r : [4947177727 / 10000000000, -7329441791 / 10000000000, -1749289889 / 2000000000]
n : [713486387 / 2000000000, -882811039 / 2500000000, 200235409 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 19530844917635849543916629275241861562521920522683849601 / 39062465934853662551939920816569965847472656250000000000
Collision distance in [2828399 / 4000000, 8838747 / 12500000] ~ [0.7071, 0.7071]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [937 / 2500, 3 / 8] ~ [0.3748, 0.375]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 505334764132999174488567425967627 / 10000000000000000000000000000000000000000
rho in [22479 / 100000000, 281 / 1250000] ~ [0.00022, 0.00022]
sigma_min ^ 2 / (16 * E ^ .5) in [877969 / 734846923, 390625 / 326598632] ~ [0.00119, 0.0012]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [3687219 / 100000000, 372959 / 10000000] ~ [0.03687, 0.0373]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [3687219 / 5878775384, 1864795 / 2939387688] ~ [0.00063, 0.00063]
CD / |V| ^ .5 in [70709975 / 447213596, 70709976 / 447213595] ~ [0.15811, 0.15811]
Success: LHS < CD / |V| ^ .5
Success: existence proven