show/hide visualization coordinates
a : (-0.4759449680400001, 0.7497265928100001, -0.51278034914)
b : (0.47388691176, 1.0388145621100002, -0.63214343394)
c : (0.16893433805999997, 0.15982987101000007, -0.9987356331400001)
d : (-0.75469685084, -0.16709559938999985, -0.7986727339400002)
e : (-0.84484621474, 0.1071192968100001, 0.15876096245999988)
f : (-0.21373963404000007, 0.8263971136100001, 0.44918118545999985)
g : (-0.17099239434000002, 1.62871128391, -0.14618814994000018)
h : (0.6546587334599999, 1.3037703929100002, 0.31502073145999987)
i : (1.2995380395599998, 0.7138736710100001, -0.17093455254000012)
j : (1.11876621786, 0.4489178403100001, -1.1180987179400002)
k : (0.87430999906, -0.16888511308999987, -0.37072955364000015)
l : (0.03884981495999995, -0.7012325700899998, -0.5071570644400001)
m : (-0.8540647046400001, -0.8622419874899999, -0.08670536904000015)
n : (-1.03901882334, -0.5833005907899999, 0.8556234859599998)
o : (-0.17863071674000008, -0.07434965028999996, 0.8821045400599998)
p : (0.64610684986, 0.3164150538100001, 0.47331254885999985)
q : (0.46624858946, -0.6642463721899999, 0.39614925615999985)
r : (-0.08234116504, -1.4584116528899997, 0.13470941935999986)
s : (-0.9456410928400001, -1.5531303312900002, 0.6304327358599999)
t : (-0.18138292944, -1.0606818107899998, 1.04685069206)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'f', 'p'], ['h', 'i', 'b'], ['l', 'q', 'k'], ['q', 'p', 'o'], ['m', 'r', 's'], ['t', 'q', 'o'], ['c', 'j', 'k'], ['c', 'j', 'b'], ['f', 'e', 'a'], ['l', 'm', 'd'], ['l', 'c', 'd'], ['f', 'e', 'o'], ['n', 't', 'o'], ['n', 't', 's'], ['e', 'd', 'a'], ['l', 'c', 'k'], ['c', 'b', 'a'], ['h', 'f', 'g'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['m', 's', 'n'], ['m', 'e', 'n'], ['q', 't', 'r'], ['f', 'p', 'o'], ['h', 'i', 'p'], ['n', 'e', 'o'], ['g', 'f', 'a'], ['l', 'm', 'r'], ['q', 'p', 'k'], ['h', 'g', 'b'], ['m', 'e', 'd'], ['i', 'j', 'k'], ['l', 'q', 'r'], ['i', 'j', 'b'], ['i', 'k', 'p'], ['t', 'r', 's']]
Coordinate Data:
k : [-300481809 / 1000000000, 1639441907 / 2500000000, 9057899347 / 10000000000]
t : [1510422239 / 2000000000, 3095146921 / 2000000000, -511790311 / 1000000000]
e : [886671503 / 625000000, 3797723529 / 10000000000, 1881497093 / 5000000000]
s : [15194692829 / 10000000000, 2040021981 / 1000000000, -238430887 / 2500000000]
g : [1862051461 / 2500000000, -5709098171 / 5000000000, 681248531 / 1000000000]
q : [537898003 / 5000000000, 11511380219 / 10000000000, 1389111249 / 10000000000]
h : [-404152717 / 5000000000, -1021098429 / 1250000000, 137524781 / 625000000]
c : [101223463 / 250000000, 3270617787 / 10000000000, 7668980071 / 5000000000]
l : [5349783751 / 10000000000, 5940621099 / 5000000000, 2084434891 / 2000000000]
p : [-361393299 / 5000000000, 1704765959 / 10000000000, 308739161 / 5000000000]
j : [-2724690139 / 5000000000, 189869047 / 5000000000, 1653159099 / 1000000000]
i : [-1451419699 / 2000000000, -2269820213 / 10000000000, 882493667 / 1250000000]
a : [10497731581 / 10000000000, -2628349431 / 10000000000, 5239203651 / 5000000000]
b : [999412783 / 10000000000, -1379807281 / 2500000000, 233440763 / 200000000]
f : [7875678241 / 10000000000, -3395054639 / 10000000000, 214697989 / 2500000000]
m : [14278928947 / 10000000000, 3372834093 / 2500000000, 6217657501 / 10000000000]
d : [13285250409 / 10000000000, 6539872491 / 10000000000, 266746623 / 200000000]
o : [1881147267 / 2500000000, 5612413 / 10000000, -347044159 / 1000000000]
r : [6561693551 / 10000000000, 9726516513 / 5000000000, 4003509617 / 10000000000]
n : [8064235067 / 5000000000, 2140384481 / 2000000000, -3205631049 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 15381602628121035191463676926478446989064517448787548830249 / 24498169495418183856435793637468207333325000000000000000000
Collision distance in [15847617 / 20000000, 39619043 / 50000000] ~ [0.79238, 0.79238]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5301 / 10000, 5303 / 10000] ~ [0.5301, 0.5303]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 2371512536839837350711 / 2500000000000000000000000000000000000000
rho in [973963559 / 1000000000000000000, 10973963559 / 1000000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [28100601 / 11757550768, 28121809 / 11757550752] ~ [0.00239, 0.00239]
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, 10061 / 50000000] ~ [-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, 10061 / 2939387688] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [79238085 / 447213596, 79238086 / 447213595] ~ [0.17718, 0.17718]
Success: LHS < CD / |V| ^ .5
Success: existence proven