show/hide visualization coordinates
a : (0.12473481460000002, 0.7801286038200002, -1.1795845595849999)
b : (-0.6615395837, 0.35992770222000015, -0.7265903291849999)
c : (-0.14101175649999997, 1.07644943232, -0.26221182918499997)
d : (0.7757207413, 1.2783927409200002, -0.606915219785)
e : (0.9523171356, 0.3248928346200002, -0.8511520761849999)
f : (0.11708476039999999, -0.2039325451799998, -1.001918773385)
g : (-0.8083870126999999, -0.5817535715799999, -1.0293645208850002)
h : (-0.9341969118, -0.3405697902799999, -0.067074412385)
i : (-0.8941525342000001, 0.6192190034200001, 0.21077792091500003)
j : (-0.019268917800000007, 0.7531566165200001, 0.676223270515)
k : (0.5322065731, 1.5138981496200001, 0.333955681215)
l : (0.7793796008, 0.5731012962200002, 0.10199280721500004)
m : (0.6793710480999999, -0.3770564234799999, -0.193301278285)
n : (-0.15645247780000004, -0.9051111611799999, -0.343491915085)
o : (-0.5908200806999999, -1.0528982887799998, 0.545037066015)
p : (-0.5356042174, -0.09180046497999983, 0.815669993815)
q : (0.4617169118, -0.12059343707999981, 0.7484276707149999)
r : (0.4056772282, -1.0780305984799998, 0.465278176915)
s : (-0.06659879899999999, -1.7434927414799999, 1.043305417115)
t : (-0.0201765223, -0.78392735718, 1.3209369095149999)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['g', 'f', 'b'], ['r', 's', 'o'], ['h', 'i', 'b'], ['h', 'n', 'g'], ['n', 'r', 'o'], ['t', 'p', 'o'], ['c', 'i', 'j'], ['c', 'j', 'k'], ['n', 'f', 'g'], ['f', 'b', 'a'], ['i', 'j', 'p'], ['m', 'f', 'n'], ['f', 'e', 'a'], ['l', 'q', 'j'], ['l', 'j', 'k'], ['e', 'd', 'a'], ['c', 'b', 'a'], ['m', 'r', 'q'], ['l', 'm', 'e'], ['q', 'j', 'p'], ['l', 'd', 'k'], ['c', 'd', 'a'], ['m', 'r', 'n'], ['q', 't', 'r'], ['h', 'p', 'o'], ['t', 's', 'o'], ['h', 'i', 'p'], ['c', 'd', 'k'], ['m', 'f', 'e'], ['h', 'n', 'o'], ['t', 'q', 'p'], ['h', 'g', 'b'], ['c', 'i', 'b'], ['l', 'e', 'd'], ['t', 'r', 's'], ['l', 'q', 'm']]
Coordinate Data:
k : [-322502259 / 5000000000, -1933792631 / 2000000000, 965071669 / 10000000000]
t : [1219706609 / 2500000000, 13309291913 / 10000000000, -4452370307 / 5000000000]
e : [-4846110143 / 10000000000, 444217999 / 2000000000, 12816149243 / 10000000000]
s : [5343049203 / 10000000000, 5726236439 / 2500000000, -612842569 / 1000000000]
g : [638046567 / 500000000, 11287554057 / 10000000000, 1459827369 / 1000000000]
q : [11978419 / 2000000000, 834494089 / 1250000000, -1589824113 / 5000000000]
h : [14019030331 / 10000000000, 2218929061 / 2500000000, 995074521 / 2000000000]
c : [3043589389 / 5000000000, -2647237991 / 5000000000, 6926746773 / 10000000000]
l : [-623346959 / 2000000000, -260994621 / 10000000000, 3284700409 / 10000000000]
p : [10033103387 / 10000000000, 6388022991 / 10000000000, -3852071457 / 10000000000]
j : [4869750391 / 10000000000, -128846739 / 625000000, -19200033 / 78125000]
i : [2723717311 / 2000000000, -722171693 / 10000000000, 274606159 / 1250000000]
a : [3429713067 / 10000000000, -2331267697 / 10000000000, 16100474077 / 10000000000]
b : [225849141 / 200000000, 1870741319 / 10000000000, 11570531773 / 10000000000]
f : [3506213609 / 10000000000, 7509343793 / 10000000000, 2864763243 / 2000000000]
m : [-529162317 / 2500000000, 577536411 / 625000000, 389852579 / 625000000]
d : [-15400731 / 50000000, -1828477267 / 2500000000, 10373780679 / 10000000000]
o : [529263101 / 500000000, 15999001229 / 10000000000, -1145742179 / 10000000000]
r : [620288931 / 10000000000, 8125162163 / 5000000000, -43519161 / 1250000000]
n : [6241585991 / 10000000000, 14521129953 / 10000000000, 483721727 / 625000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 125000000007929846723319173019987122210633122125197944758121 / 250000000029833534812966330919133771584750000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2619 / 5000, 131 / 250] ~ [0.5238, 0.524]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 9119142689044177471501 / 10000000000000000000000000000000000000000
rho in [954942023 / 1000000000000000000, 10954942023 / 1000000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [6859161 / 2939387692, 858050 / 367423461] ~ [0.00233, 0.00234]
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, 20123 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-9995 / 2939387688, 20123 / 5878775376] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [35355339 / 223606798, 70710679 / 447213595] ~ [0.15811, 0.15811]
Success: LHS < CD / |V| ^ .5
Success: existence proven