show/hide visualization coordinates
a : (0.6645316793210525, 0.4382416786368421, -0.39160055417894735)
b : (0.7315961201210526, -0.505057499763158, -0.7166990035789473)
c : (0.023833501221052544, 0.10022570203684211, -1.0809850739789473)
d : (-0.10669607227894745, 1.006383898536842, -0.6786923607789472)
e : (-0.0020626095789474386, 0.7545180832368421, 0.2833970012210527)
f : (0.7859601808210526, 0.21227738643684207, 0.5749369707210527)
g : (1.4312922395210526, -0.13610918336315792, -0.1048963437789473)
h : (0.7152349420210525, -0.7331283236631579, 0.2568080677210527)
i : (0.13268237682105255, -1.2333941631631578, -0.38379056897894737)
j : (0.015206636021052544, -0.8733256453631578, -1.3092904953789473)
k : (-0.5548522215789475, -0.5297026384631579, -0.5629955598789473)
l : (-0.8859046786789475, 0.3881718117368421, -0.7818806621789474)
m : (-0.8860636182789474, 1.075997506436842, -0.05600486147894734)
n : (-0.7891700765789476, 0.7952327599368421, 0.8988680275210527)
o : (0.10125814622105256, 0.4994705607368421, 1.2447897655210527)
p : (0.31863474442105255, -0.47058677156315787, 1.1364558540210528)
q : (-0.2775500088789475, -0.7300053359631579, 0.37667578172105265)
r : (-0.7838461347789476, 0.10785611293684211, 0.1725863371210527)
s : (-0.6340851458789476, -0.16706593936315794, 1.1223176786210527)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['d', 'a', 'c'], ['o', 'p', 'f'], ['d', 'a', 'e'], ['k', 'i', 'q'], ['l', 'k', 'r'], ['s', 'r', 'n'], ['s', 'n', 'o'], ['h', 'p', 'q'], ['h', 'p', 'f'], ['b', 'j', 'i'], ['l', 'k', 'c'], ['b', 'g', 'a'], ['m', 'e', 'n'], ['i', 'h', 'q'], ['r', 'm', 'n'], ['e', 'n', 'o'], ['s', 'p', 'o'], ['k', 'r', 'q'], ['b', 'a', 'c'], ['g', 'h', 'f'], ['j', 'k', 'i'], ['l', 'd', 'c'], ['d', 'e', 'm'], ['f', 'e', 'o'], ['d', 'm', 'l'], ['b', 'j', 'c'], ['b', 'g', 'h'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['l', 'r', 'm'], ['s', 'r', 'q'], ['g', 'a', 'f'], ['s', 'q', 'p']]
Coordinate Data:
d : [5846698427 / 10000000000, -4303022779 / 10000000000, 11710581581 / 10000000000]
c : [1135350673 / 2500000000, 2379279593 / 5000000000, 15733508713 / 10000000000]
n : [1267143847 / 1000000000, -2191511393 / 10000000000, -2032511151 / 5000000000]
s : [11120589163 / 10000000000, 18578689 / 25000000, -6299518813 / 10000000000]
q : [7555237793 / 10000000000, 6530434783 / 5000000000, 289225039 / 2500000000]
p : [79669513 / 500000000, 5233341961 / 5000000000, -6440900567 / 10000000000]
i : [215807121 / 625000000, 9047378919 / 5000000000, 8761563663 / 10000000000]
m : [13640373887 / 10000000000, -2499579429 / 5000000000, 1370926647 / 2500000000]
a : [-1865579089 / 10000000000, 68919971 / 500000000, 1767932703 / 2000000000]
b : [-2536223497 / 10000000000, 2702847801 / 2500000000, 12090648009 / 10000000000]
e : [24001819 / 50000000, -892182313 / 5000000000, 2089687961 / 10000000000]
r : [3154549763 / 2500000000, 4682255077 / 10000000000, 1598897301 / 5000000000]
j : [289229459 / 625000000, 724703633 / 500000000, 18016562927 / 10000000000]
k : [129103249 / 125000000, 11057842591 / 10000000000, 2638403393 / 2500000000]
l : [13638784491 / 10000000000, 1879098089 / 10000000000, 2548492919 / 2000000000]
h : [-593152929 / 2500000000, 13092099443 / 10000000000, 147223581 / 625000000]
f : [-384983013 / 1250000000, 1819021171 / 5000000000, -412855867 / 5000000000]
g : [-9533184691 / 10000000000, 178047701 / 250000000, 5972621411 / 10000000000]
o : [1883578121 / 5000000000, 766110599 / 10000000000, -3762119841 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 7968371710144817341780931005596734042348770169855753725489 / 15618237048427516990600903800657180835217187500000000000000
Collision distance in [4464253 / 6250000, 71428049 / 100000000] ~ [0.71428, 0.71428]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [3183 / 10000, 637 / 2000] ~ [0.3183, 0.3185]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 26850022703808613992548098389 / 10000000000000000000000000000000000000000
rho in [32771953 / 20000000000000, 32971953 / 20000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [10131489 / 11426285488, 1449175 / 1632326496] ~ [0.00089, 0.00089]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [4703 / 50000000, 9921 / 20000000] ~ [9e-05, 0.0005]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [4703 / 2856571372, 16535 / 1904380912] ~ [0.0, 1e-05]
CD / |V| ^ .5 in [71428048 / 435889895, 6493459 / 39626354] ~ [0.16387, 0.16387]
Success: LHS < CD / |V| ^ .5
Success: existence proven