show/hide visualization coordinates
a : (-0.7194038923588237, 0.6436407961823531, -0.11417078192941177)
b : (-0.02721495905882365, 0.450126055082353, 0.5811180252705882)
c : (0.25161849704117634, 0.722271111982353, -0.3398537288294118)
d : (-0.3364255111588237, 0.10961823798235298, -0.8679263567294118)
e : (-0.7296996426588237, -0.35553280261764697, -0.0748500888294118)
f : (-1.4800702697588237, 0.16846995658235303, 0.32809535447058824)
g : (-0.9199373174588237, 0.810869833782353, 0.8511378704705882)
h : (-0.7394673966588237, -0.171069088217647, 0.9079406971705882)
i : (0.08452580834117629, -0.5380633299176469, 0.4762574516705883)
j : (0.8130224084411762, 0.08134025228235303, 0.18362815387058817)
k : (1.2415329090411764, 0.6956031524823532, -0.4789877532294118)
l : (0.6574620843411764, 0.007118909982352983, -0.9089304464294118)
m : (0.09629190414117628, -0.716761434717647, -0.5075761452294117)
n : (-1.5651176527588238, 0.21042605978235301, 1.3235885127705882)
o : (0.9087818131411763, -0.904281566517647, 0.04441692347058823)
p : (1.5020815855411764, -0.269437957117647, -0.4505264789294118)
q : (0.9620196318411763, -0.944338187017647, -0.9533612090294118)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'o', 'm'], ['d', 'l', 'c'], ['b', 'j', 'c'], ['i', 'e', 'm'], ['o', 'q', 'm'], ['f', 'h', 'e'], ['k', 'p', 'j'], ['n', 'g', 'f'], ['q', 'l', 'p'], ['i', 'b', 'h'], ['d', 'l', 'm'], ['d', 'e', 'm'], ['i', 'o', 'j'], ['i', 'h', 'e'], ['d', 'c', 'a'], ['b', 'g', 'a'], ['g', 'f', 'a'], ['l', 'q', 'm'], ['d', 'e', 'a'], ['b', 'g', 'h'], ['k', 'l', 'p'], ['f', 'e', 'a'], ['i', 'b', 'j'], ['n', 'g', 'h'], ['k', 'l', 'c'], ['p', 'o', 'q'], ['c', 'b', 'a'], ['n', 'f', 'h'], ['o', 'p', 'j'], ['k', 'j', 'c']]
Coordinate Data:
a : [-674600699 / 5000000000, 10997675949 / 10000000000, 2240124813 / 5000000000]
g : [-3354535649 / 10000000000, 506798653 / 400000000, 282666723 / 200000000]
q : [3866258461 / 2500000000, -4882113883 / 10000000000, -782330929 / 2000000000]
i : [6690095609 / 10000000000, -12802583 / 156250000, 5192265981 / 5000000000]
m : [6807756567 / 10000000000, -65158659 / 250000000, 546195993 / 10000000000]
c : [261281953 / 312500000, 11783979107 / 10000000000, 2223420157 / 10000000000]
j : [1397506161 / 1000000000, 537467051 / 1000000000, 932279873 / 1250000000]
o : [14932655657 / 10000000000, -2240773839 / 5000000000, 151653167 / 250000000]
h : [-1549836441 / 10000000000, 570115421 / 2000000000, 14701364417 / 10000000000]
k : [2282520827 / 1250000000, 1439662439 / 1250000000, 832079913 / 10000000000]
p : [20865653381 / 10000000000, 58340263 / 312500000, 69793291 / 625000000]
n : [-4903169501 / 5000000000, 1333105717 / 2000000000, 18857842573 / 10000000000]
d : [1240291207 / 5000000000, 5657450367 / 10000000000, -1528653061 / 5000000000]
b : [1114537587 / 2000000000, 4531264269 / 5000000000, 5716568849 / 5000000000]
e : [-1452158901 / 10000000000, 1005939961 / 10000000000, 4873456557 / 10000000000]
l : [12419458369 / 10000000000, 4632457087 / 10000000000, -3467347019 / 10000000000]
f : [-2238966293 / 2500000000, 6245967553 / 10000000000, 890291099 / 1000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 1250000000230427061645284186594392414466710550586142304569 / 2500000000603544013302518083236370935192000000000000000000
Collision distance in [35355339 / 50000000, 70710679 / 100000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2771 / 5000, 693 / 1250] ~ [0.5542, 0.5544]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 2627507157669345122849 / 2500000000000000000000000000000000000000
rho in [10251843 / 10000000000000000, 110251843 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [7678441 / 2683281576, 1920996 / 670820393] ~ [0.00286, 0.00286]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19991 / 100000000, 20107 / 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 [-19991 / 5366563144, 20107 / 5366563144] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [70710678 / 412310563, 70710679 / 412310562] ~ [0.1715, 0.1715]
Success: LHS < CD / |V| ^ .5
Success: existence proven