show/hide visualization coordinates
a : (1.84995529694, -0.06305700176500012, -1.0253455876250002)
b : (1.3609127827399998, 0.5292285897349999, -0.38501189962500015)
c : (2.3579884200400003, 0.4645586987349999, -0.3445024795250002)
d : (2.7711991672400003, 0.2657726550349999, -1.2331703005250003)
e : (2.6408379550400003, -0.4684610334650001, -0.5669088792250002)
f : (1.7946462387399997, -0.31040325826500015, -0.05801646642500019)
g : (0.9789771947399999, -0.3606794103650001, -0.6343647761250002)
h : (0.36957690703999996, 0.40176402723499993, -0.41681248022500017)
i : (0.9064705507399999, -0.03151249606500012, 0.3071079499749998)
j : (0.14239366553999994, -0.5227999422650002, -0.1110104251250002)
k : (-0.58738567086, 0.12350128673499983, -0.3340393694250002)
l : (-0.03323375106000004, 0.2590267066349998, 0.4872668199749999)
m : (-0.68835174706, -0.49530110046500014, 0.44497022927499985)
n : (-1.4939907840600002, -0.20842652556500013, -0.07334553632500018)
o : (-1.01499156786, 0.4476441633349999, 0.5098225442749997)
p : (-1.54407379996, -0.2942500986650001, 0.9217141649749998)
q : (-2.35287378626, -0.4770412651650001, 0.36277127817499977)
r : (-2.01370877406, 0.45857970543499993, 0.46052760327499986)
s : (-2.44640874336, -4.845606500014643e-05, 1.2366983698749998)
t : (-2.99793955426, 0.2819047552349999, 0.45164924037499987)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['n', 'm', 'k'], ['p', 'n', 'm'], ['e', 'd', 'c'], ['t', 's', 'q'], ['p', 'r', 's'], ['o', 'k', 'l'], ['o', 'n', 'r'], ['o', 'r', 'p'], ['e', 'd', 'a'], ['m', 'k', 'j'], ['h', 'b', 'i'], ['g', 'a', 'f'], ['b', 'i', 'f'], ['g', 'i', 'j'], ['h', 'k', 'j'], ['h', 'i', 'l'], ['i', 'j', 'l'], ['m', 'j', 'l'], ['e', 'c', 'f'], ['o', 'n', 'k'], ['n', 'r', 'q'], ['t', 'r', 's'], ['g', 'h', 'b'], ['e', 'a', 'f'], ['b', 'c', 'a'], ['b', 'c', 'f'], ['p', 's', 'q'], ['g', 'h', 'j'], ['g', 'b', 'a'], ['d', 'c', 'a'], ['g', 'i', 'f'], ['o', 'm', 'p'], ['o', 'm', 'l'], ['t', 'r', 'q'], ['p', 'n', 'q'], ['h', 'k', 'l']]
Coordinate Data:
s : [-19665710773 / 10000000000, 2318373103 / 5000000000, 17697894689 / 10000000000]
d : [32510368333 / 10000000000, 7294957317 / 10000000000, -1400158403 / 2000000000]
p : [-10642361339 / 10000000000, 84736489 / 500000000, 90925329 / 62500000]
m : [-208514081 / 1000000000, -157890119 / 5000000000, 9780613283 / 10000000000]
q : [-9365180601 / 5000000000, -26636377 / 2000000000, 2239655943 / 2500000000]
e : [31206756211 / 10000000000, -2961223 / 625000000, -169088901 / 5000000000]
h : [8494145731 / 10000000000, 8654871039 / 10000000000, 290696547 / 2500000000]
f : [2843104881 / 1250000000, 191649773 / 1250000000, 2375373163 / 5000000000]
n : [-507076559 / 500000000, 2552965511 / 10000000000, 4597455627 / 10000000000]
a : [2329792963 / 1000000000, 4006660749 / 10000000000, -2461272443 / 5000000000]
g : [113969911 / 78125000, 1030436663 / 10000000000, -1012736771 / 10000000000]
b : [2300938061 / 1250000000, 1241189583 / 1250000000, 740395997 / 5000000000]
l : [89320783 / 200000000, 7227497833 / 10000000000, 1020357919 / 1000000000]
r : [-383467777 / 250000000, 9223027821 / 10000000000, 9936187023 / 10000000000]
t : [-12590509441 / 5000000000, 7456278319 / 10000000000, 4923701697 / 5000000000]
c : [28378260861 / 10000000000, 4641408877 / 5000000000, 377177239 / 2000000000]
j : [1555578329 / 2500000000, -36923041 / 625000000, 4220806739 / 10000000000]
o : [-2675769509 / 5000000000, 22784181 / 25000000, 10429136433 / 10000000000]
i : [1732885271 / 1250000000, 2161052903 / 5000000000, 840199049 / 1000000000]
k : [-67217503 / 625000000, 2936121817 / 5000000000, 124407331 / 625000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 19999273005656134781074404156382385862726963084520669461649 / 40003107089375033918861754799489340485228000000000000000000
Collision distance in [35353323 / 50000000, 70706647 / 100000000] ~ [0.70707, 0.70707]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2697 / 10000, 2699 / 10000] ~ [0.2697, 0.2699]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 102984386637269452338534815436431 / 2000000000000000000000000000000000000000
rho in [22691 / 100000000, 5673 / 25000000] ~ [0.00023, 0.00023]
sigma_min ^ 2 / (16 * E ^ .5) in [7273809 / 11757550768, 7284601 / 11757550752] ~ [0.00062, 0.00062]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [5483503 / 100000000, 2764453 / 50000000] ~ [0.05484, 0.05529]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [5483503 / 5878775384, 2764453 / 2939387688] ~ [0.00093, 0.00094]
CD / |V| ^ .5 in [35353323 / 223606798, 70706647 / 447213595] ~ [0.1581, 0.1581]
Success: LHS < CD / |V| ^ .5
Success: existence proven