show/hide visualization coordinates
a : (-0.34433396820526313, -0.5305721831105263, -0.5399252257631579)
b : (-1.017548045005263, 0.11427847218947368, -0.1780544767631579)
c : (-0.7732536314052629, 0.13794959508947363, -1.147466627263158)
d : (0.16756910699473693, -0.1573920450105264, -1.3136770122631578)
e : (0.6228985100947368, -0.7567363224105262, -0.655299028163158)
f : (0.24066059919473692, -0.6488339928105263, 0.2624434559368421)
g : (-0.7539486407052631, -0.6871639158105264, 0.3587932226368421)
h : (-0.886797320105263, 0.19528868828947366, 0.8100455141368421)
i : (-0.42346269050526314, 0.8291558775894736, 0.1907447741368421)
j : (-0.9367468288052629, 0.9910857007894737, -0.6520589556631579)
k : (-0.014742737605263068, 0.6062129931894736, -0.694266216263158)
l : (0.898765317494737, 0.20128022868947365, -0.7334130156631579)
m : (1.580824537294737, -0.5244064375105263, -0.8238236560631579)
n : (1.169268422194737, -0.33323772201052637, 0.06728581323684207)
o : (0.7539062893947369, -0.14504139341052635, 0.9572613312368421)
p : (-0.18510229080526314, -0.4352812192105263, 1.141716550236842)
q : (-0.588784624505263, 0.23562021018947366, 1.7637550093368421)
r : (0.02603733559473692, 0.5362935279894736, 1.034653154736842)
s : (0.4647906593947369, 0.37149993728947367, 0.15128538823684207)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['r', 'q', 'p'], ['d', 'a', 'c'], ['o', 'p', 'f'], ['d', 'a', 'e'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['l', 's', 'n'], ['o', 'n', 'f'], ['r', 's', 'i'], ['s', 'r', 'o'], ['k', 's', 'i'], ['l', 'k', 's'], ['s', 'n', 'o'], ['h', 'p', 'q'], ['r', 'p', 'o'], ['d', 'k', 'c'], ['b', 'j', 'i'], ['b', 'g', 'a'], ['m', 'e', 'n'], ['b', 'a', 'c'], ['j', 'k', 'i'], ['e', 'n', 'f'], ['r', 'h', 'i'], ['b', 'j', 'c'], ['b', 'g', 'h'], ['g', 'p', 'f'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['l', 'm', 'e'], ['g', 'h', 'p'], ['r', 'h', 'q'], ['l', 'm', 'n'], ['g', 'a', 'f']]
Coordinate Data:
d : [1445141971 / 5000000000, 5468518959 / 10000000000, 4387916221 / 2500000000]
c : [6149255663 / 5000000000, 1257551279 / 5000000000, 7944780517 / 5000000000]
n : [-712670921 / 1000000000, 7226975729 / 10000000000, 3742036629 / 10000000000]
s : [-40965791 / 5000000000, 5612473 / 312500000, 2902040879 / 10000000000]
q : [10453821257 / 10000000000, 1538396407 / 10000000000, -3305663833 / 2500000000]
p : [40106237 / 62500000, 8247410701 / 10000000000, -7002270741 / 10000000000]
i : [8800601917 / 10000000000, -4396960267 / 10000000000, 125372351 / 500000000]
m : [-11242270361 / 10000000000, 2284665721 / 2500000000, 6326565661 / 5000000000]
a : [4004657347 / 5000000000, 460016017 / 500000000, 9814147019 / 10000000000]
b : [7370727731 / 5000000000, 2751813787 / 10000000000, 6195439529 / 10000000000]
r : [538200207 / 1250000000, -1468336771 / 10000000000, -2965818393 / 5000000000]
e : [-1663010089 / 10000000000, 11461961733 / 10000000000, 10967885043 / 10000000000]
j : [139334433 / 100000000, -6016258499 / 10000000000, 5467742159 / 5000000000]
k : [1178350597 / 2500000000, -2167531423 / 10000000000, 2839389231 / 2500000000]
l : [-4421678163 / 10000000000, 940898111 / 5000000000, 5874512459 / 5000000000]
h : [13433948213 / 10000000000, 970855813 / 5000000000, -184278019 / 500000000]
f : [107968451 / 500000000, 10382938437 / 10000000000, 895230101 / 5000000000]
g : [12105461419 / 10000000000, 10766237667 / 10000000000, 165392507 / 2000000000]
o : [-1486543941 / 5000000000, 5345012443 / 10000000000, -5157718551 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 124999999049908775768251394815393812021943016647602297628249 / 250000000647002432133878825144004551107850000000000000000000
Collision distance in [70710677 / 100000000, 35355339 / 50000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [463 / 1250, 1853 / 5000] ~ [0.3704, 0.3706]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 6700936951650875268991299 / 2000000000000000000000000000000000000000
rho in [578832313 / 10000000000000000, 678832313 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [857476 / 714142843, 3433609 / 2856571368] ~ [0.0012, 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 [-4777 / 25000000, 2631 / 12500000] ~ [-0.00019, 0.00021]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-4777 / 1428285684, 877 / 238047614] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710677 / 435889895, 35355339 / 217944947] ~ [0.16222, 0.16222]
Success: LHS < CD / |V| ^ .5
Success: existence proven