show/hide visualization coordinates
a : (0.19904749344999995, -0.07835734618000001, -0.93283972156)
b : (0.60825080655, 0.76255961532, -0.57870512536)
c : (1.11384216345, 0.19594193852000003, -1.22933696296)
d : (0.97938727215, -0.68219764858, -0.7702152494600001)
e : (0.14144688234999997, -0.7931148526799999, -0.23584339696)
f : (-0.6909539364499999, -0.34670087657999993, -0.56420819236)
g : (-0.37065500105000004, 0.59505524802, -0.46171920026)
h : (0.16823412024999995, 0.9607436459200001, 0.29714212483999997)
i : (1.16508174395, 0.98496818182, 0.22159090523999997)
j : (1.2922142403499999, 0.11181122922000003, -0.2489771177600001)
k : (1.02488704255, -0.72557346288, 0.22780694943999996)
l : (0.17744245714999995, -0.6620432046799999, 0.7548758071399999)
m : (-0.6980026533500001, -0.84011452658, 0.30555803243999996)
n : (-1.5604262795500001, -0.58183696668, -0.12977883816000002)
o : (-1.3344050569500001, 0.37542543452, -0.31023133046000007)
p : (-0.82664135455, 0.89687831372, 0.37552585493999996)
q : (-0.24420142055000005, 0.23934424032, 0.85345123134)
r : (0.7092832445499999, 0.16253472752000003, 0.5619597359399999)
s : (-0.6762729223500001, -0.5625866254799999, 1.2660298345399998)
t : (-1.17755884195, -0.012737064580000013, 0.59791465944)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['f', 'o', 'n'], ['l', 'k', 'e'], ['i', 'j', 'b'], ['p', 'h', 'g'], ['f', 'm', 'n'], ['f', 'm', 'e'], ['t', 'm', 'n'], ['o', 't', 'p'], ['p', 'h', 'q'], ['m', 'l', 's'], ['d', 'c', 'a'], ['d', 'j', 'c'], ['d', 'e', 'k'], ['t', 'q', 's'], ['b', 'a', 'g'], ['d', 'e', 'a'], ['f', 'a', 'g'], ['f', 'e', 'a'], ['d', 'j', 'k'], ['c', 'a', 'b'], ['j', 'c', 'b'], ['l', 'm', 'e'], ['t', 'm', 's'], ['r', 'q', 'l'], ['o', 't', 'n'], ['r', 'j', 'i'], ['p', 't', 'q'], ['h', 'r', 'i'], ['p', 'o', 'g'], ['f', 'o', 'g'], ['q', 'l', 's'], ['l', 'k', 'r'], ['i', 'h', 'b'], ['h', 'q', 'r'], ['r', 'k', 'j'], ['g', 'h', 'b']]
Coordinate Data:
s : [11628210779 / 10000000000, 82863413 / 78125000, -149405853 / 200000000]
d : [-2464195583 / 5000000000, 2360525419 / 2000000000, 1289215819 / 1000000000]
k : [-538338887 / 1000000000, 6118192619 / 5000000000, 2911936201 / 10000000000]
r : [-222735089 / 1000000000, 1677651667 / 5000000000, -26849479 / 625000000]
n : [20469744351 / 10000000000, 2699755069 / 2500000000, 6487794077 / 10000000000]
j : [-503541303 / 625000000, 3862538317 / 10000000000, 7679776873 / 10000000000]
a : [2875006621 / 10000000000, 5764224071 / 10000000000, 14518402911 / 10000000000]
o : [145676257 / 80000000, 153299533 / 1250000000, 8292319 / 10000000]
m : [11845508089 / 10000000000, 107054367 / 80000000, 2134425371 / 10000000000]
b : [-121702651 / 1000000000, -330618193 / 1250000000, 10977056949 / 10000000000]
l : [386382123 / 1250000000, 362533833 / 312500000, -294844047 / 1250000000]
q : [7307495761 / 10000000000, 1293604103 / 5000000000, -1672253309 / 5000000000]
f : [294375523 / 250000000, 2703251 / 3200000, 10832087619 / 10000000000]
i : [-1696333971 / 2500000000, -4869031209 / 10000000000, 2974096643 / 10000000000]
p : [13131895101 / 10000000000, -249258283 / 625000000, 717373573 / 5000000000]
g : [4286015783 / 5000000000, -969901871 / 10000000000, 4903598849 / 5000000000]
e : [862753183 / 2500000000, 403493723 / 312500000, 1509687933 / 2000000000]
t : [665642799 / 400000000, 1021604251 / 2000000000, -789140899 / 10000000000]
h : [3183140353 / 10000000000, -92535717 / 200000000, 2218584447 / 10000000000]
c : [-6272940079 / 10000000000, 377653903 / 1250000000, 699335013 / 400000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 22206378921350173155287693793488813570368806805765098477601 / 35492841465039016700080591380625746234088000000000000000000
Collision distance in [79098543 / 100000000, 4943659 / 6250000] ~ [0.79099, 0.79099]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [231 / 500, 2311 / 5000] ~ [0.462, 0.4622]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 8396021287753746406807 / 5000000000000000000000000000000000000000
rho in [129584113 / 100000000000000000, 1129584113 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [1334025 / 734846923, 5340721 / 2939387688] ~ [0.00182, 0.00182]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-1249 / 6250000, 1259 / 6250000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-1249 / 367423461, 1259 / 367423461] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [79098543 / 447213596, 79098544 / 447213595] ~ [0.17687, 0.17687]
Success: LHS < CD / |V| ^ .5
Success: existence proven