show/hide visualization coordinates
a : (0.272087154755, -0.805256115555, -0.14742507126000015)
b : (-0.692951299045, -0.971415189255, 0.055286423139999874)
c : (-0.281017058445, -1.360156993055, -0.7688434105600002)
d : (0.28704149885499997, -0.6207130613549999, -1.13013572876)
e : (0.7923650785549999, -0.028551486654999958, -0.5024473181600001)
f : (0.7541299810550001, -0.19642270345499996, 0.48261985433999977)
g : (-0.07418945434500002, -0.670615687255, 0.7809953409399999)
h : (-1.062664290045, -0.567980772155, 0.89227684944)
i : (-1.011311323845, -0.023445325755000024, 0.05511257553999982)
j : (-0.627525149545, -0.42215275115499995, -0.7777983218600002)
k : (-0.0018743621450000303, 0.327071481545, -0.9951094877600002)
l : (0.506506246655, 0.920702030045, -0.3712890567600001)
m : (1.297370093155, 0.563475086145, 0.12562469943999988)
n : (1.226802077655, 0.419666804245, 1.11271097464)
o : (0.35002246035499995, 0.01502192424500004, 1.3725570938399998)
p : (-0.47668277274500004, 0.24159965544500006, 0.85756099654)
q : (-0.404860111545, 0.7705014938450001, 0.011922572839999868)
r : (-0.959427611645, 0.5211516967450001, -0.7819789129600001)
s : (-0.300140582445, 1.270142708245, -0.8479567661600002)
t : (0.40631942475499994, 0.6173772051449999, 0.5763166935399999)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'i', 'b'], ['r', 'i', 'j'], ['c', 'j', 'd'], ['t', 'p', 'o'], ['r', 'j', 'k'], ['e', 'd', 'k'], ['h', 'p', 'g'], ['c', 'j', 'b'], ['n', 'f', 'o'], ['l', 't', 'm'], ['q', 'i', 'p'], ['m', 'f', 'n'], ['f', 'e', 'a'], ['n', 't', 'o'], ['e', 'd', 'a'], ['c', 'b', 'a'], ['q', 'r', 's'], ['l', 'm', 'e'], ['m', 't', 'n'], ['c', 'd', 'a'], ['g', 'b', 'a'], ['o', 'p', 'g'], ['r', 's', 'k'], ['j', 'd', 'k'], ['h', 'i', 'p'], ['q', 'r', 'i'], ['l', 'q', 's'], ['g', 'f', 'a'], ['l', 'e', 'k'], ['m', 'f', 'e'], ['t', 'q', 'p'], ['l', 'q', 't'], ['h', 'g', 'b'], ['g', 'f', 'o'], ['i', 'j', 'b'], ['l', 's', 'k']]
Coordinate Data:
k : [2786130013 / 5000000000, 4361554377 / 5000000000, -3399768533 / 10000000000]
t : [1930839579 / 2000000000, 1162616599 / 1000000000, 76965583 / 62500000]
e : [13514654433 / 10000000000, 161464971 / 312500000, 1526853163 / 10000000000]
s : [2589597823 / 10000000000, 18153821021 / 10000000000, -1928241317 / 10000000000]
g : [303069319 / 625000000, -626881467 / 5000000000, 7180639877 / 5000000000]
q : [385600633 / 2500000000, 13157408877 / 10000000000, 6670552073 / 10000000000]
h : [-5035639253 / 10000000000, -227413783 / 10000000000, 15474094839 / 10000000000]
c : [2780833063 / 10000000000, -1018646999 / 1250000000, -1137107761 / 10000000000]
l : [5328033057 / 5000000000, 14659414239 / 10000000000, 2838435777 / 10000000000]
p : [10302199 / 125000000, 7868390493 / 10000000000, 1512693631 / 1000000000]
j : [-85530981 / 1250000000, 1230866427 / 10000000000, -613328437 / 5000000000]
i : [-4522109591 / 10000000000, 5217940681 / 10000000000, 71024521 / 100000000]
a : [1662375039 / 2000000000, -2600167217 / 10000000000, 317317227 / 625000000]
b : [-1338509343 / 10000000000, -2130878977 / 5000000000, 444011911 / 625000000]
f : [6566151729 / 5000000000, 436020863 / 1250000000, 1422190611 / 1250000000]
m : [18564704579 / 10000000000, 13858931 / 12500000, 7807573339 / 10000000000]
d : [2115354659 / 2500000000, -30189467 / 400000000, -4750030943 / 10000000000]
o : [9091228251 / 10000000000, 5602613181 / 10000000000, 20276897283 / 10000000000]
r : [-4003272469 / 10000000000, 5331955453 / 5000000000, -253692557 / 2000000000]
n : [2232378053 / 1250000000, 9649061981 / 10000000000, 17678436091 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 437191639790084993831198861206350643616482453203904053368689 / 989186261363433669441640904355745626925800000000000000000000
Collision distance in [66480899 / 100000000, 664809 / 1000000] ~ [0.66481, 0.66481]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [487 / 1250, 1949 / 5000] ~ [0.3896, 0.3898]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 5598114803711632125674887 / 2000000000000000000000000000000000000000
rho in [529061187 / 10000000000000000, 629061187 / 10000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [948676 / 734846923, 3798601 / 2939387688] ~ [0.00129, 0.00129]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19203 / 100000000, 419 / 2000000] ~ [-0.00019, 0.00021]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-6401 / 1959591792, 10475 / 2939387688] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [66480899 / 447213596, 13296180 / 89442719] ~ [0.14866, 0.14866]
Success: LHS < CD / |V| ^ .5
Success: existence proven