show/hide visualization coordinates
a : (0.5444107933352941, 0.012744600276470841, 0.9323952811235294)
b : (0.8429301135352941, 0.46925147007647083, 0.09424989202352935)
c : (-0.08357823786470592, 0.6159852582764708, 0.4407343364235294)
d : (-0.4124532321647059, -0.25201995642352915, 0.8127668425235295)
e : (0.2807123438352941, -0.5782640247235291, 0.17004894532352938)
f : (1.247695320335294, -0.4062754223235292, 0.3581017224235294)
g : (1.5232431273352942, 0.03479579147647083, -0.4960233212764706)
h : (0.5662305900352941, 0.07696281787647086, -0.7829883804764706)
i : (0.16582620193529407, 0.938990813376471, -0.4722086171764706)
j : (-0.790056893264706, 0.9576695813764707, -0.17905573477647058)
k : (-1.049617836764706, 0.5062334651764709, 0.6746617536235295)
l : (-1.378039717564706, -0.43725039202352917, 0.6301951446235294)
m : (-0.6891527550647059, -0.6443086080235292, -0.06447142887647062)
n : (0.0056377539352940875, -0.7510967928235291, -0.7757114930764706)
o : (0.9709957973352942, -0.7985640738235291, -0.5191365486764706)
p : (-0.4184660087647059, 0.14120065917647084, -0.6209818747764706)
q : (-1.326317360164706, 0.11394481307647086, -0.2025765189764706)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['b', 'f', 'a'], ['n', 'p', 'm'], ['g', 'f', 'o'], ['n', 'h', 'p'], ['k', 'q', 'j'], ['n', 'e', 'm'], ['i', 'p', 'j'], ['n', 'o', 'e'], ['i', 'b', 'h'], ['d', 'l', 'm'], ['d', 'e', 'm'], ['b', 'g', 'f'], ['i', 'j', 'c'], ['i', 'h', 'p'], ['d', 'k', 'l'], ['q', 'p', 'j'], ['i', 'b', 'c'], ['d', 'c', 'a'], ['n', 'h', 'o'], ['l', 'q', 'm'], ['d', 'e', 'a'], ['d', 'k', 'c'], ['g', 'o', 'h'], ['b', 'g', 'h'], ['f', 'o', 'e'], ['p', 'q', 'm'], ['f', 'e', 'a'], ['k', 'l', 'q'], ['c', 'b', 'a'], ['k', 'j', 'c']]
Coordinate Data:
g : [20669627011 / 10000000000, 3438314763 / 5000000000, -2694257 / 625000000]
q : [-978247233 / 1250000000, 3834059871 / 5000000000, 2891359911 / 10000000000]
e : [1030539897 / 1250000000, 186507841 / 2500000000, 3308807277 / 5000000000]
i : [7095457757 / 10000000000, 3183715949 / 2000000000, 195038929 / 10000000000]
m : [-1454331813 / 10000000000, 85585531 / 10000000000, 1068102703 / 2500000000]
k : [-505898263 / 1000000000, 11591006263 / 10000000000, 11663742637 / 10000000000]
h : [5549750819 / 5000000000, 729829979 / 1000000000, -182047419 / 625000000]
o : [15147153711 / 10000000000, -1456969127 / 10000000000, -137120193 / 5000000000]
p : [25050713 / 200000000, 7940678203 / 10000000000, -1292693647 / 10000000000]
j : [-492674639 / 2000000000, 644214697 / 400000000, 3126567753 / 10000000000]
c : [4601413359 / 10000000000, 6344262097 / 5000000000, 1864893693 / 2000000000]
n : [5493573277 / 10000000000, -982296317 / 10000000000, -283998983 / 1000000000]
d : [164082927 / 1250000000, 4008472047 / 10000000000, 6522396763 / 5000000000]
b : [13866496873 / 10000000000, 1402648289 / 1250000000, 5859624021 / 10000000000]
a : [10881303671 / 10000000000, 3328058807 / 5000000000, 1780134739 / 1250000000]
l : [-4171600719 / 5000000000, 2156167691 / 10000000000, 11219076547 / 10000000000]
f : [17914148941 / 10000000000, 616479347 / 2500000000, 339925693 / 400000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 18257315436909960570581797013903053709733806888626923 / 31122525255357239302715438091747831036171875000000000
Collision distance in [38295791 / 50000000, 76591583 / 100000000] ~ [0.76592, 0.76592]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [4021 / 10000, 4023 / 10000] ~ [0.4021, 0.4023]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 296857056525327971631271 / 2500000000000000000000000000000000000000
rho in [5448459 / 500000000000000, 10448459 / 500000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [16168441 / 10733126304, 16184529 / 10733126288] ~ [0.00151, 0.00151]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-3971 / 20000000, 20279 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-19855 / 5366563144, 20279 / 5366563144] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [76591582 / 412310563, 76591583 / 412310562] ~ [0.18576, 0.18576]
Success: LHS < CD / |V| ^ .5
Success: existence proven