show/hide visualization coordinates
a : (0.6589543395666667, 0.056677137953333345, 1.1813371909466668)
b : (0.6154655670666667, 0.46448326355333336, 0.2693039914466667)
c : (0.7365926491666667, 1.0477032218533333, 1.0725385131466667)
d : (1.2180642540666666, 0.5873366425533334, 1.8183591140466668)
e : (0.2215708602666667, 0.6678856171533334, 1.8409738705466667)
f : (-0.13998725203333334, 0.5941756469533334, 0.9115436415466667)
g : (0.019696299966666664, -0.3041458753466667, 0.5022535096466667)
h : (0.3441951871666667, -0.18972927454666666, -0.4366870826533333)
i : (-0.32883926433333327, 0.44633389295333337, -0.05926807145333324)
j : (-0.5920996068333333, -0.4961775372466667, -0.26509577145333324)
k : (-0.10589344313333332, -0.8073230468466667, -1.0816680045533331)
l : (-0.40419445663333337, 0.14442499625333333, -1.0096226941533333)
m : (-1.0789877040333333, -0.5829859621466668, -1.1342339979533331)
n : (-0.6972504442333332, -1.2942431132466665, -1.7244787402533333)
o : (-0.46728698603333335, -0.33441560984666663, -1.8852554688533334)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'f', 'g'], ['a', 'd', 'e'], ['j', 'k', 'm'], ['k', 'n', 'm'], ['b', 'f', 'i'], ['o', 'k', 'n'], ['b', 'h', 'i'], ['d', 'c', 'e'], ['b', 'h', 'g'], ['a', 'b', 'g'], ['j', 'h', 'k'], ['h', 'i', 'l'], ['a', 'b', 'c'], ['l', 'h', 'k'], ['a', 'f', 'e'], ['a', 'c', 'd'], ['e', 'c', 'f'], ['j', 'i', 'g'], ['b', 'c', 'f'], ['j', 'l', 'm'], ['o', 'l', 'k'], ['o', 'l', 'm'], ['o', 'n', 'm'], ['j', 'h', 'g'], ['a', 'f', 'g'], ['j', 'i', 'l']]
Coordinate Data:
e : [540051517 / 2500000000, -645439373 / 5000000000, -1418000813 / 1000000000]
m : [15165791711 / 10000000000, 11217837047 / 10000000000, 3114414111 / 2000000000]
o : [9048784531 / 10000000000, 2183033381 / 2500000000, 1442642829 / 625000000]
h : [933962799 / 10000000000, 7285270171 / 10000000000, 4298300701 / 5000000000]
g : [4178951671 / 10000000000, 8429436179 / 10000000000, -792804521 / 10000000000]
a : [-88545149 / 400000000, 2410603023 / 5000000000, -3791820667 / 5000000000]
l : [8417859237 / 10000000000, 3943727463 / 10000000000, 14325957517 / 10000000000]
d : [-780472787 / 1000000000, -485389 / 10000000, -2790772113 / 2000000000]
c : [-2990011821 / 10000000000, -5089054793 / 10000000000, -1623913639 / 2500000000]
n : [11348419113 / 10000000000, 9165204279 / 5000000000, 10737258989 / 5000000000]
j : [10296910739 / 10000000000, 5174876399 / 5000000000, 688068829 / 1000000000]
b : [-1778741 / 10000000, 74314479 / 1000000000, 1536690661 / 10000000000]
k : [2717424551 / 5000000000, 6730603947 / 5000000000, 15046410621 / 10000000000]
i : [3832153657 / 5000000000, 28894953 / 312500000, 482241129 / 1000000000]
f : [5775787191 / 10000000000, -138444761 / 2500000000, -61071323 / 125000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 15
|E| = 39
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 166666381619027239717895082376101534493405540224971828972523 / 333335155102881914986578440563688479516600000000000000000000
Collision distance in [8838803 / 12500000, 2828417 / 4000000] ~ [0.7071, 0.7071]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [433 / 1000, 1083 / 2500] ~ [0.433, 0.4332]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 324317673277308719597534082057 / 2000000000000000000000000000000000000000
rho in [63670801 / 5000000000000, 63720801 / 5000000000000] ~ [1e-05, 1e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [187489 / 99919968, 1172889 / 624499799] ~ [0.00188, 0.00188]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [127109 / 100000000, 83647 / 50000000] ~ [0.00127, 0.00167]
LHS DEN := 8 * |E| ^ .5 in [624499799 / 12500000, 3122499 / 62500] ~ [49.95998, 49.95998]
LHS := (LHS NUM) / (LHS DEN) in [127109 / 4995998400, 83647 / 2497999196] ~ [3e-05, 3e-05]
CD / |V| ^ .5 in [70710424 / 387298335, 70710425 / 387298334] ~ [0.18257, 0.18257]
Success: LHS < CD / |V| ^ .5
Success: existence proven