show/hide visualization coordinates
a : (-0.07609071296000008, 0.8474162387549998, 0.5824433840049998)
b : (0.9114721035399999, 0.777509771655, 0.4416010981049999)
c : (0.42873558644, 1.616466777455, 0.19037859980499994)
d : (-0.53170896986, 1.727064011655, 0.44593055740499987)
e : (-1.06246432716, 0.8799054973549999, 0.42115195520499993)
f : (-0.62620500026, 0.017991613454999944, 0.6795675394049998)
g : (0.3669043208399999, -0.04910913154500007, 0.5835280751049998)
h : (0.9479723648399999, 0.03395487875499992, -0.2260771217950001)
i : (0.6771444969399999, 0.952290311955, -0.514716410495)
j : (-0.25936223696000005, 0.9841149609549998, -0.1655087760950001)
k : (-0.86053266116, 0.1927721831549999, -0.2767504621950001)
l : (-1.18876172366, -0.6368564293450001, 0.17488921620499986)
m : (-0.21460971586000005, -0.8161210323450001, 0.3123493414049999)
n : (0.77465225454, -0.865623762345, 0.17482042660499997)
o : (0.54032456764, -0.690843235645, -0.7814970485950001)
p : (0.061061554339999935, 0.17901315705499998, -0.6646513832950001)
q : (-0.3978809336600001, -0.679422395245, -0.43560155869500006)
r : (-0.80231344256, -1.522749567945, -0.08171204629500006)
s : (0.16975383863999993, -1.4937643193449999, -0.3146014022950001)
t : (1.1419086363399997, -1.4540095284449999, -0.5455439834950001)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['n', 'm', 's'], ['a', 'e', 'f'], ['h', 'n', 'g'], ['o', 'q', 's'], ['r', 'q', 'l'], ['n', 't', 'o'], ['r', 'q', 's'], ['a', 'c', 'd'], ['m', 'f', 'l'], ['a', 'f', 'g'], ['p', 'k', 'j'], ['r', 'm', 'l'], ['i', 'c', 'j'], ['p', 'i', 'h'], ['a', 'e', 'd'], ['a', 'b', 'c'], ['p', 'o', 'h'], ['k', 'q', 'p'], ['k', 'e', 'f'], ['m', 's', 'r'], ['e', 'j', 'd'], ['b', 'i', 'c'], ['d', 'c', 'j'], ['m', 'f', 'g'], ['k', 'e', 'j'], ['n', 'm', 'g'], ['a', 'b', 'g'], ['o', 'q', 'p'], ['b', 'h', 'g'], ['n', 'o', 'h'], ['k', 'q', 'l'], ['i', 'j', 'p'], ['n', 't', 's'], ['o', 't', 's'], ['b', 'i', 'h'], ['k', 'f', 'l']]
Coordinate Data:
o : [10692654639 / 10000000000, -2393258383 / 10000000000, -296547057 / 1250000000]
d : [-865023 / 312500000, 2178581409 / 1000000000, 2475474901 / 2500000000]
p : [2950012253 / 5000000000, 788163193 / 1250000000, -1203919803 / 10000000000]
t : [8354247663 / 5000000000, -10024921311 / 10000000000, -2569161 / 2000000000]
l : [-3299104137 / 5000000000, -23167379 / 125000000, 449467887 / 625000000]
j : [2695786593 / 10000000000, 14356323583 / 10000000000, 3787506269 / 10000000000]
g : [8958452171 / 10000000000, 2012041329 / 5000000000, 11277874781 / 10000000000]
m : [785827951 / 2500000000, -72920727 / 200000000, 2141521861 / 2500000000]
k : [-3315917649 / 10000000000, 1288579161 / 2000000000, 2612392 / 9765625]
i : [3015213483 / 2500000000, 14038077093 / 10000000000, 11817197 / 400000000]
r : [-2733725463 / 10000000000, -5356160853 / 5000000000, 4625473567 / 10000000000]
s : [6986947349 / 10000000000, -521123461 / 500000000, 2296580007 / 10000000000]
b : [7202064999 / 5000000000, 1229027169 / 1000000000, 9858605011 / 10000000000]
e : [-5335234309 / 10000000000, 13314228947 / 10000000000, 4827056791 / 5000000000]
a : [4528501833 / 10000000000, 12989336361 / 10000000000, 1126702787 / 1000000000]
f : [-12158013 / 125000000, 1173772527 / 2500000000, 764891839 / 625000000]
c : [9576764827 / 10000000000, 5169960437 / 2500000000, 1836595007 / 2500000000]
n : [3258982877 / 2500000000, -82821273 / 200000000, 898849787 / 1250000000]
q : [655299813 / 5000000000, -2279049979 / 10000000000, 1086578443 / 10000000000]
h : [14769132611 / 10000000000, 4854722761 / 10000000000, 795455703 / 2500000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 3652337263337473350205310296016991110202590612978806961089 / 9623111590283927337173275983624228265235000000000000000000
Collision distance in [61606661 / 100000000, 30803331 / 50000000] ~ [0.61607, 0.61607]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1839 / 5000, 46 / 125] ~ [0.3678, 0.368]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 257281567273171853373967024693 / 312500000000000000000000000000000000000
rho in [1120829 / 39062500000, 8969757 / 312500000000] ~ [3e-05, 3e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [3381921 / 2939387692, 423200 / 367423461] ~ [0.00115, 0.00115]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [441263 / 100000000, 481679 / 100000000] ~ [0.00441, 0.00482]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [441263 / 5878775384, 481679 / 5878775376] ~ [8e-05, 8e-05]
CD / |V| ^ .5 in [61606661 / 447213596, 61606662 / 447213595] ~ [0.13776, 0.13776]
Success: LHS < CD / |V| ^ .5
Success: existence proven