show/hide visualization coordinates
a : (0.26051694175500006, -0.9845093329749999, -0.7331610365850001)
b : (0.6836791021549999, -0.4066129625749999, -0.035328986085000125)
c : (-0.026921303244999972, -1.0616489966749998, 0.22152672771499993)
d : (-0.5182559649449999, -0.4524174079749999, -0.40090971188500013)
e : (-0.32491023094499993, -0.4971166229749999, -1.3810216478850001)
f : (0.5463834106550001, -0.8816910221749998, -1.685898543485)
g : (1.0716720370550001, -0.4438943831749999, -0.9562370042850001)
h : (0.6921179549550001, 0.41319556982500005, -0.6079045320850001)
i : (0.406645885455, 0.47423884002500005, 0.3485364836149999)
j : (0.27088081495500005, -0.3653265092749999, 0.8745572721149998)
k : (-0.685207812645, -0.4017620127749999, 0.5837532312149999)
l : (-0.563639616745, 0.43726230892500006, 0.053414319514999864)
m : (-0.26397067264499996, 0.37676006632500003, -0.8987085729850002)
n : (0.46145408185500003, 0.10242007852500012, -1.529974362285)
o : (0.054649892754999985, 1.1282779346250003, -0.3210392654850001)
p : (-0.23783323514499996, 1.1837264204250002, 0.6336224993149998)
q : (0.10717615725500007, 0.5240879046250001, 1.301339166515)
r : (-0.46091015734499996, -0.2610283438749999, 1.5480584714149996)
s : (-0.8489124702449999, 0.4876524011250002, 1.0105351257149997)
t : (-0.6246148149449999, 0.628386070025, 1.9748403659149996)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'p', 'o'], ['h', 'i', 'b'], ['l', 's', 'p'], ['h', 'n', 'g'], ['q', 'r', 'j'], ['r', 'j', 'k'], ['q', 's', 'p'], ['h', 'i', 'o'], ['c', 'j', 'k'], ['q', 't', 's'], ['c', 'j', 'b'], ['n', 'f', 'g'], ['q', 'i', 'p'], ['t', 'r', 's'], ['f', 'e', 'a'], ['q', 'i', 'j'], ['l', 'm', 'd'], ['e', 'd', 'a'], ['n', 'f', 'e'], ['c', 'b', 'a'], ['l', 'd', 'k'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['m', 'e', 'n'], ['q', 't', 'r'], ['h', 'm', 'o'], ['l', 'm', 'o'], ['r', 's', 'k'], ['g', 'f', 'a'], ['c', 'd', 'k'], ['l', 'o', 'p'], ['h', 'g', 'b'], ['m', 'e', 'd'], ['i', 'j', 'b'], ['h', 'n', 'm'], ['l', 's', 'k']]
Coordinate Data:
k : [-2348101923 / 10000000000, 61382443 / 500000000, 2105990931 / 2000000000]
t : [-871085973 / 5000000000, 1441141211 / 1250000000, 12220413001 / 5000000000]
e : [627436947 / 5000000000, 137051379 / 5000000000, -1139724267 / 1250000000]
s : [-3985148499 / 10000000000, 10121792999 / 10000000000, 18497217 / 12500000]
g : [7610348287 / 5000000000, 201581289 / 2500000000, -48699477 / 100000000]
q : [348483611 / 625000000, 5243074017 / 5000000000, 2213226751 / 1250000000]
h : [11425155753 / 10000000000, 4688612343 / 5000000000, -693311489 / 5000000000]
c : [4234763171 / 10000000000, -5371220979 / 10000000000, 345384481 / 500000000]
l : [-283104991 / 2500000000, 9617892077 / 10000000000, 2613282769 / 5000000000]
p : [531410963 / 2500000000, 2135316649 / 1250000000, 1378580917 / 1250000000]
j : [7212784353 / 10000000000, 318400779 / 2000000000, 1679749383 / 1250000000]
i : [4285217529 / 5000000000, 2496914347 / 2500000000, 8177787179 / 10000000000]
a : [7109145621 / 10000000000, -2299912171 / 5000000000, -2639188023 / 10000000000]
b : [453630689 / 400000000, 589569681 / 5000000000, 2169566241 / 5000000000]
f : [996781031 / 1000000000, -1785820617 / 5000000000, -3041640773 / 2500000000]
m : [1864269477 / 10000000000, 9012869651 / 10000000000, -4294663387 / 10000000000]
d : [-339291723 / 5000000000, 180273727 / 2500000000, 85415653 / 1250000000]
o : [5050475131 / 10000000000, 8264024167 / 5000000000, 185253711 / 1250000000]
r : [-10512537 / 1000000000, 2634985549 / 10000000000, 20173007057 / 10000000000]
n : [4559258511 / 5000000000, 6269469773 / 10000000000, -33147879 / 31250000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 5952380950813780283759285392919474818598399835286040179701 / 11904761903775895604256027400643261433575000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1163 / 2500, 2327 / 5000] ~ [0.4652, 0.4654]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 215413396217022367273 / 200000000000000000000000000000000000000
rho in [103781837 / 100000000000000000, 1103781837 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [1352569 / 734846923, 5414929 / 2939387688] ~ [0.00184, 0.00184]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19987 / 100000000, 1007 / 5000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-19987 / 5878775376, 5035 / 1469693844] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [35355339 / 223606798, 70710679 / 447213595] ~ [0.15811, 0.15811]
Success: LHS < CD / |V| ^ .5
Success: existence proven