show/hide visualization coordinates
a : (0.4844971742789474, 0.6312617588473685, 0.628380053031579)
b : (0.7212180905789474, -0.2277893761526315, 0.17451404303157897)
c : (0.6761902793789474, 0.6205525894473685, -0.35301643516842107)
d : (-0.2653555945210526, 0.7107535616473685, -0.028431851768421113)
e : (-0.3921405868210526, 1.0179187315473683, 0.914741050731579)
f : (0.20799195337894738, 0.5865368327473685, 1.5883511690315788)
g : (0.1964380221789474, -0.2400520404526315, 1.025663563731579)
h : (0.15490055957894738, -1.0201397613526315, 0.4013737377315789)
i : (0.30402275467894735, -0.7695576546526315, -0.555167520468421)
j : (1.0979733519789474, -0.19404043495263157, -0.751183792168421)
k : (0.7872466154789474, 0.5487522545473684, -1.344233465968421)
l : (-0.08111639932105263, 0.29414294654736844, -0.918651776368421)
m : (-0.8081092872210526, -0.07047538935263153, -0.33681433336842104)
n : (-1.0800088948210527, 0.43526085554736843, 0.48190506543157896)
o : (-0.6627352710210527, 0.15788862074736842, 1.347322517331579)
p : (-0.6628916144210527, -0.46944979565263156, 0.568575776231579)
q : (-0.6062403860210527, -1.0457341850526316, -0.246707573768421)
r : (-0.4942587222210526, -0.5915302490526315, -1.130539510068421)
s : (0.42237795487894736, -0.37429926495263155, -1.4660807171684211)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['d', 'a', 'c'], ['d', 'a', 'e'], ['l', 's', 'r'], ['d', 'm', 'n'], ['r', 's', 'i'], ['l', 'k', 's'], ['r', 'i', 'q'], ['j', 's', 'i'], ['h', 'p', 'q'], ['n', 'm', 'p'], ['n', 'p', 'o'], ['b', 'j', 'i'], ['l', 'k', 'c'], ['b', 'g', 'a'], ['i', 'h', 'q'], ['e', 'n', 'o'], ['b', 'a', 'c'], ['l', 'd', 'c'], ['g', 'p', 'o'], ['f', 'e', 'o'], ['d', 'm', 'l'], ['b', 'j', 'c'], ['k', 's', 'j'], ['m', 'p', 'q'], ['o', 'g', 'f'], ['b', 'g', 'h'], ['d', 'e', 'n'], ['a', 'e', 'f'], ['b', 'i', 'h'], ['k', 'j', 'c'], ['g', 'h', 'p'], ['l', 'r', 'm'], ['r', 'm', 'q'], ['g', 'a', 'f']]
Coordinate Data:
d : [1489633781 / 2000000000, -1703459333 / 10000000000, 1744992613 / 2500000000]
c : [-983644917 / 5000000000, -801449611 / 10000000000, 5112908143 / 5000000000]
n : [3898675477 / 2500000000, 65716733 / 625000000, 5864379 / 31250000]
s : [570833411 / 10000000000, 9147068933 / 10000000000, 10678229553 / 5000000000]
q : [542850841 / 500000000, 7930709067 / 5000000000, 1145340959 / 1250000000]
p : [713970569 / 625000000, 63116089 / 62500000, 252473543 / 2500000000]
i : [1754385413 / 10000000000, 1309965283 / 1000000000, 12247327139 / 10000000000]
m : [1609463229 / 1250000000, 6108830177 / 10000000000, 2515948817 / 2500000000]
a : [-50358783 / 10000000000, -181708261 / 2000000000, 102962851 / 2500000000]
b : [-1208783973 / 5000000000, 1536394009 / 2000000000, 309406969 / 625000000]
e : [2179004707 / 2500000000, -596888879 / 1250000000, -2451758573 / 10000000000]
r : [4868600091 / 5000000000, 5659689387 / 5000000000, 3600209407 / 2000000000]
j : [-77314007 / 125000000, 7344480633 / 10000000000, 221992029 / 156250000]
k : [-615570639 / 2000000000, -41723131 / 5000000000, 10068993297 / 5000000000]
l : [5605776953 / 10000000000, 1231323409 / 5000000000, 7941084849 / 5000000000]
h : [811401841 / 2500000000, 15605473897 / 10000000000, 2681914557 / 10000000000]
f : [1357346713 / 5000000000, -115323011 / 2500000000, -2296964939 / 2500000000]
g : [1415116369 / 5000000000, 487787293 / 625000000, -3560983703 / 10000000000]
o : [1142196567 / 1000000000, 956297519 / 2500000000, -6777573239 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 2491378326494308608133343900184079407639953336589627383401 / 4255920614281108438487495467065787993676000000000000000000
Collision distance in [76510859 / 100000000, 3825543 / 5000000] ~ [0.76511, 0.76511]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [2631 / 5000, 329 / 625] ~ [0.5262, 0.5264]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 538349000190825815219 / 500000000000000000000000000000000000000
rho in [103764059 / 100000000000000000, 1103764059 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [6922161 / 2856571372, 123704 / 51010203] ~ [0.00242, 0.00243]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-19989 / 100000000, 503 / 2500000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-6663 / 1904380912, 2515 / 714142842] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [76510859 / 435889895, 38255430 / 217944947] ~ [0.17553, 0.17553]
Success: LHS < CD / |V| ^ .5
Success: existence proven