show/hide visualization coordinates
a : (0.18590807462941167, -0.03241443701764701, 1.0245769490941177)
b : (1.1252978226294117, -0.257932545317647, 0.7663358717941177)
c : (0.6630746734294117, 0.520390485382353, 0.34140876619411764)
d : (0.1609961338294117, 0.965575662482353, 1.0828447524941176)
e : (-0.6917043895705882, 0.446936908482353, 1.0202693011941175)
f : (-0.48418869517058827, -0.222621539917647, 0.3070871291941176)
g : (0.3608541894294117, -0.7550879781176469, 0.35589411879411764)
h : (0.9894222684294116, -0.236986196817647, -0.22416857220588238)
i : (0.1886916047294117, 0.29035322458235296, -0.5083227638058824)
j : (-0.2768186921705883, 0.828538027882353, 0.19428477079411766)
k : (-1.2042225394705883, 0.45590363548235296, 0.16163977269411767)
l : (-1.0489278409705882, -0.261720525517647, -0.5172556758058823)
m : (-0.16427973787058836, -0.7274326685176471, -0.49467595890588234)
n : (0.7320921077294117, -1.170282824217647, -0.4746452672058823)
o : (0.5606792600294117, -0.416904285517647, -1.1094983525058821)
p : (-0.37677900207058834, -0.09351801341764698, -1.2383131387058826)
q : (-0.7200952375705884, 0.667203070082353, -0.6874617031058824)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['d', 'j', 'c'], ['k', 'e', 'j'], ['f', 'l', 'm'], ['i', 'q', 'p'], ['k', 'q', 'j'], ['i', 'h', 'c'], ['o', 'p', 'm'], ['i', 'h', 'o'], ['p', 'l', 'q'], ['d', 'e', 'j'], ['n', 'o', 'm'], ['i', 'o', 'p'], ['k', 'f', 'l'], ['i', 'j', 'c'], ['d', 'c', 'a'], ['n', 'h', 'o'], ['b', 'g', 'a'], ['k', 'f', 'e'], ['g', 'f', 'a'], ['d', 'e', 'a'], ['b', 'g', 'h'], ['n', 'g', 'm'], ['l', 'p', 'm'], ['b', 'h', 'c'], ['f', 'e', 'a'], ['g', 'f', 'm'], ['n', 'g', 'h'], ['i', 'q', 'j'], ['k', 'l', 'q'], ['c', 'b', 'a']]
Coordinate Data:
a : [65140841 / 200000000, 2892797929 / 5000000000, -5063699561 / 10000000000]
g : [753790451 / 5000000000, 13012331269 / 10000000000, 811564371 / 5000000000]
q : [3079268793 / 2500000000, -1210579213 / 10000000000, 12056686961 / 10000000000]
i : [3229206749 / 10000000000, 1278959621 / 5000000000, 320790549 / 312500000]
m : [270356807 / 400000000, 12735778173 / 10000000000, 10128829519 / 10000000000]
c : [-757311969 / 5000000000, 128773317 / 5000000000, 441995567 / 2500000000]
j : [3942154859 / 5000000000, -2823928791 / 10000000000, 1619611111 / 5000000000]
k : [17158348191 / 10000000000, 902415133 / 10000000000, 3565672203 / 10000000000]
p : [8883912817 / 10000000000, 3198315811 / 5000000000, 17565201317 / 10000000000]
h : [-298631243 / 625000000, 489457091 / 625000000, 1855938913 / 2500000000]
o : [-122667451 / 2500000000, 9630494343 / 10000000000, 3255410691 / 2000000000]
n : [-2204798281 / 10000000000, 1716427973 / 1000000000, 4964261301 / 5000000000]
d : [1753080729 / 5000000000, -4194305137 / 10000000000, -1129275519 / 2000000000]
b : [-613685543 / 1000000000, 8040776941 / 10000000000, -620322197 / 2500000000]
e : [3008291673 / 2500000000, 992082403 / 10000000000, -2510311541 / 5000000000]
l : [7802700603 / 5000000000, 8078656743 / 10000000000, 80895521 / 78125000]
f : [2489502437 / 2500000000, 7687666887 / 10000000000, 1055599319 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 17
|E| = 45
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 8339260133142584297567408338657439747701056595704056753329 / 15524170884772636066069990437156096371568750000000000000000
Collision distance in [36646251 / 50000000, 73292503 / 100000000] ~ [0.73293, 0.73293]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [3413 / 10000, 683 / 2000] ~ [0.3413, 0.3415]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1871789115038387424731788957 / 10000000000000000000000000000000000000000
rho in [432641781 / 1000000000000000, 442641781 / 1000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [11648569 / 10733126304, 11662225 / 10733126288] ~ [0.00109, 0.00109]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-13201 / 100000000, 26961 / 100000000] ~ [-0.00013, 0.00027]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [-13201 / 5366563144, 26961 / 5366563144] ~ [-0.0, 1e-05]
CD / |V| ^ .5 in [73292502 / 412310563, 73292503 / 412310562] ~ [0.17776, 0.17776]
Success: LHS < CD / |V| ^ .5
Success: existence proven