show/hide visualization coordinates
a : (-0.030022082249999915, 0.30532896669, -0.9162448519999999)
b : (-0.7356827172499999, 0.9743533692899999, -1.1495887051)
c : (-0.12828198704999993, 1.13873330749, -0.372386275)
d : (0.4376413324500001, 0.38600892388999997, -0.036027998800000016)
e : (0.6791695537500001, -0.3532598343100001, -0.6646342586)
f : (-0.2511367983499999, -0.4620221844100001, -0.3143474343)
g : (-0.9356356218499998, 0.24383701358999993, -0.49662260860000007)
h : (-1.5865618066500002, 0.9921253176899999, -0.6245278503)
i : (-0.9202356076499999, 1.73070234449, -0.5219929519000001)
j : (-0.96429325025, 0.99903671039, 0.15824545689999997)
k : (-0.07273139404999995, 0.95477043859, 0.6089759208)
l : (0.2953756193500001, 0.07266572308999997, 0.9028950553999999)
m : (0.9263560338500001, -0.41822449251000005, 0.30215342359999997)
n : (1.39851361315, -0.9840851168100001, -0.3737674568)
o : (0.4576824411500001, -1.1214928253100003, -0.06400000630000002)
p : (-0.16810176724999992, -0.77133381991, 0.6329811834)
q : (-0.5853106403499998, 0.11476342448999993, 0.4310693671)
r : (0.6658294907500001, -0.8128539731100001, 1.1832853953)
s : (1.2212032292500001, -1.34302276421, 0.5425974852)
t : (0.29622235925000007, -1.64603052911, 0.77193711)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['f', 'p', 'q'], ['o', 'e', 'n'], ['q', 'j', 'g'], ['k', 'j', 'c'], ['m', 'r', 's'], ['o', 't', 'p'], ['d', 'm', 'l'], ['d', 'c', 'a'], ['r', 'm', 'l'], ['b', 'a', 'g'], ['p', 't', 'r'], ['d', 'e', 'a'], ['m', 'e', 'n'], ['o', 's', 'n'], ['k', 'q', 'l'], ['f', 'a', 'g'], ['f', 'e', 'a'], ['t', 'r', 's'], ['f', 'q', 'g'], ['k', 'q', 'j'], ['m', 's', 'n'], ['d', 'k', 'c'], ['o', 't', 's'], ['h', 'j', 'i'], ['c', 'a', 'b'], ['i', 'c', 'b'], ['d', 'm', 'e'], ['p', 'q', 'l'], ['r', 'p', 'l'], ['f', 'o', 'e'], ['h', 'j', 'g'], ['d', 'l', 'k'], ['i', 'h', 'b'], ['f', 'o', 'p'], ['j', 'c', 'i'], ['g', 'h', 'b']]
Coordinate Data:
s : [-5310479003 / 10000000000, 18103928419 / 10000000000, -1370238409 / 10000000000]
d : [505027993 / 2000000000, 406805769 / 5000000000, 4416016431 / 10000000000]
k : [762886723 / 1000000000, -4874003609 / 10000000000, -406804553 / 2000000000]
r : [121629191 / 5000000000, 3200560127 / 2500000000, -777711751 / 1000000000]
n : [-3541791421 / 5000000000, 2902910389 / 2000000000, 7793411011 / 10000000000]
j : [517015181 / 312500000, -5316666327 / 10000000000, 1236640937 / 5000000000]
a : [225055441 / 312500000, 162041111 / 1000000000, 13218184963 / 10000000000]
o : [1162364439 / 5000000000, 1588862903 / 1000000000, 2347868253 / 5000000000]
b : [7129190231 / 5000000000, -1267458229 / 2500000000, 7775811747 / 5000000000]
m : [-2362007049 / 10000000000, 4427972851 / 5000000000, 1034202207 / 10000000000]
q : [12754659693 / 10000000000, 881516633 / 2500000000, -63739307 / 2500000000]
l : [493474637 / 1250000000, 1973521773 / 5000000000, -4973214111 / 10000000000]
f : [9412921273 / 10000000000, 9293922621 / 10000000000, 3599605393 / 5000000000]
p : [4291285481 / 5000000000, 48386871 / 39062500, -2274075391 / 10000000000]
i : [8051954683 / 5000000000, -3158330667 / 2500000000, 4637832981 / 5000000000]
g : [4064477377 / 2500000000, 2235330641 / 10000000000, 9021962529 / 10000000000]
e : [13732219 / 1250000000, 102578739 / 125000000, 10702079029 / 10000000000]
t : [3939329697 / 10000000000, 5283501517 / 2500000000, -3663634657 / 10000000000]
h : [5691792839 / 2500000000, -13118881 / 25000000, 5150507473 / 5000000000]
c : [204609329 / 250000000, -3356816149 / 5000000000, 7779599193 / 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 = 6084332417078870911295903145795117581298665939586787374243 / 13256634648309111090744503200813759131500000000000000000000
Collision distance in [67746961 / 100000000, 33873481 / 50000000] ~ [0.67747, 0.67747]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [143 / 400, 3577 / 10000] ~ [0.3575, 0.3577]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 238008669366712968254403069 / 2000000000000000000000000000000000000000
rho in [5390157 / 15625000000000, 5546407 / 15625000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [12780625 / 11757550768, 12794929 / 11757550752] ~ [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 [-1433 / 10000000, 12919 / 50000000] ~ [-0.00014, 0.00026]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-7165 / 2939387688, 12919 / 2939387688] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [67746961 / 447213596, 67746962 / 447213595] ~ [0.15149, 0.15149]
Success: LHS < CD / |V| ^ .5
Success: existence proven