show/hide visualization coordinates
a : (-0.3572577603999999, 1.0855437359736841, -0.5146386110736842)
b : (-1.0561263518, 1.0446582844736843, 0.1994411959263157)
c : (-0.09580245759999989, 0.8879462867736841, 0.43013458132631566)
d : (0.5751215156000001, 0.7910377610736842, -0.3050318410736843)
e : (0.0005178030000001499, 0.23937287937368423, -0.9095949773736842)
f : (-0.6459113686999999, 0.20126855017368417, -0.14757253497368428)
g : (-1.2004140461, 0.18210092917368426, 0.6843893316263158)
h : (-0.7797035676999999, 0.9567999773736843, 1.1564529400263157)
i : (-0.26584807259999993, 0.10794489947368424, 1.0323656728263155)
j : (0.5240254106000001, 0.10328584427368415, 0.41911347422631573)
k : (1.2163428584, 0.023713330673684196, -0.2980788406736843)
l : (0.9458749375000001, 0.44144986177368417, -1.1654561695736843)
m : (0.6742770800000001, -0.4980687893263158, -0.9567958147736844)
n : (-0.17548848029999992, -0.6291143693263158, -0.4461825867736843)
o : (-0.6372652526999999, -0.6074583961263158, 0.44054873222631574)
p : (0.24858889930000005, -0.7370100663263157, 0.8860582429263156)
q : (0.7102530363, -0.7854995624263158, 0.0003296819263156614)
r : (0.38220654890000005, -1.4193712375263159, -0.7000933753736843)
s : (-0.06339073169999992, -1.3885999195263157, 0.19461089862631575)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['s', 'q', 'p'], ['d', 'a', 'c'], ['b', 'g', 'f'], ['h', 'i', 'c'], ['d', 'a', 'e'], ['d', 'e', 'l'], ['d', 'k', 'l'], ['o', 'n', 'f'], ['b', 'c', 'h'], ['j', 'i', 'p'], ['s', 'r', 'n'], ['s', 'n', 'o'], ['d', 'k', 'j'], ['g', 'i', 'o'], ['s', 'p', 'o'], ['m', 'e', 'n'], ['d', 'j', 'c'], ['j', 'i', 'c'], ['r', 'm', 'n'], ['l', 'k', 'm'], ['b', 'a', 'c'], ['k', 'j', 'q'], ['i', 'p', 'o'], ['e', 'n', 'f'], ['m', 'k', 'q'], ['o', 'g', 'f'], ['b', 'g', 'h'], ['a', 'e', 'f'], ['b', 'a', 'f'], ['l', 'm', 'e'], ['s', 'r', 'q'], ['r', 'm', 'q'], ['j', 'q', 'p'], ['g', 'i', 'h']]
Coordinate Data:
d : [5528875327 / 5000000000, 12271630721 / 10000000000, 1163077729 / 5000000000]
c : [2174255461 / 5000000000, 6620357989 / 5000000000, 4838909841 / 5000000000]
n : [710330139 / 2000000000, -1929890583 / 10000000000, 914648001 / 10000000000]
s : [4672628181 / 10000000000, -1904949217 / 2000000000, 1464516571 / 2000000000]
q : [12409065861 / 10000000000, -1746871257 / 5000000000, 84058917 / 156250000]
p : [7792424491 / 10000000000, -3008847553 / 10000000000, 7118528149 / 5000000000]
i : [662013693 / 2500000000, 1088140421 / 2000000000, 15700130597 / 10000000000]
m : [6024653149 / 5000000000, -619434783 / 10000000000, -4191484279 / 10000000000]
a : [866978947 / 5000000000, 1521669047 / 1000000000, 115043879 / 5000000000]
b : [-262736401 / 500000000, 2961567191 / 2000000000, 1842721457 / 2500000000]
e : [663964191 / 1250000000, 422186369 / 625000000, -743895181 / 2000000000]
r : [9128600987 / 10000000000, -1966491853 / 2000000000, -324891977 / 2000000000]
j : [2636697401 / 2500000000, 5394111553 / 10000000000, 9567608611 / 10000000000]
k : [8734982041 / 5000000000, 4598386417 / 10000000000, 1197842731 / 5000000000]
l : [14765284873 / 10000000000, 548484483 / 625000000, -6278087827 / 10000000000]
h : [-2490500179 / 10000000000, 3482313221 / 2500000000, 16941003269 / 10000000000]
f : [-1152578189 / 10000000000, 1593484653 / 2500000000, 3900748519 / 10000000000]
g : [-6697604963 / 10000000000, 3091131201 / 5000000000, 2444073437 / 2000000000]
o : [-1066117029 / 10000000000, -1713330851 / 10000000000, 9781961191 / 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 = 784491456240953518915065013068711362077403398054452609 / 1562473833845995678940156861262781722106250000000000000
Collision distance in [70857811 / 100000000, 17714453 / 25000000] ~ [0.70858, 0.70858]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [3063 / 10000, 613 / 2000] ~ [0.3063, 0.3065]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 29458440855617018530694030983 / 2000000000000000000000000000000000000000
rho in [76757333 / 20000000000000, 76957333 / 20000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [9381969 / 11426285488, 9394225 / 11426285472] ~ [0.00082, 0.00082]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [51621 / 100000000, 5741 / 6250000] ~ [0.00052, 0.00092]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [51621 / 5713142744, 5741 / 357071421] ~ [1e-05, 2e-05]
CD / |V| ^ .5 in [70857811 / 435889895, 35428906 / 217944947] ~ [0.16256, 0.16256]
Success: LHS < CD / |V| ^ .5
Success: existence proven