show/hide visualization coordinates
a : (0.5420752253529411, -0.1767422409117647, 0.598848396682353)
b : (0.572528758552941, -0.9752633421117647, -0.0023513270176469536)
c : (1.1937984892529412, -0.20747896341176467, -0.15898389411764696)
d : (1.0877171355529411, 0.6309804206882352, 0.375557570082353)
e : (0.09945192085294108, 0.7148523559882354, 0.5032241200823531)
f : (-0.3161756183470589, 0.009282742588235304, 1.0771802023823531)
g : (-0.14696878214705889, -0.8960108650117646, 0.687552859882353)
h : (-0.25371570504705887, -0.44768054941176466, -0.19995981941764696)
i : (0.5083932101529411, -0.4445981108117647, -0.8474587006176469)
j : (1.2916534455529411, -1.0469349049117647, -0.6935267630176469)
k : (0.467371435352941, 0.4413583948882353, -0.38550366261764696)
l : (-0.4230106396470589, 0.8932457799882352, -0.3305675417176469)
m : (-0.8921136345470588, 0.5853780956882353, 0.49717487538235305)
n : (-0.9933875252470589, -0.4091618896117647, 0.47195877468235303)
o : (-1.0575237218470588, 0.12150511538823533, -0.37314875841764694)
p : (-0.2745842670470589, 0.1598828355882353, -0.9940023363176469)
q : (-1.4055097267470589, 1.0473851253882354, -0.22599399591764696)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'o', 'p'], ['o', 'm', 'n'], ['h', 'g', 'n'], ['a', 'e', 'd'], ['o', 'l', 'q'], ['o', 'p', 'l'], ['i', 'b', 'j'], ['h', 'b', 'g'], ['i', 'k', 'c'], ['o', 'm', 'q'], ['c', 'b', 'j'], ['k', 'd', 'c'], ['h', 'i', 'b'], ['a', 'f', 'e'], ['b', 'a', 'g'], ['a', 'd', 'c'], ['m', 'l', 'q'], ['b', 'a', 'c'], ['k', 'p', 'l'], ['l', 'k', 'e'], ['m', 'f', 'e'], ['k', 'e', 'd'], ['h', 'i', 'p'], ['a', 'f', 'g'], ['i', 'j', 'c'], ['f', 'm', 'n'], ['f', 'g', 'n'], ['i', 'k', 'p'], ['h', 'o', 'n'], ['l', 'm', 'e']]
Coordinate Data:
d : [4271544049 / 2500000000, 1297973217 / 1250000000, 1107824717 / 1250000000]
e : [7203524049 / 10000000000, 11222505089 / 10000000000, 2534815809 / 2500000000]
j : [597673103 / 312500000, -39971047 / 62500000, -365649119 / 2000000000]
g : [4739317019 / 10000000000, -4886127121 / 10000000000, 5991275317 / 5000000000]
q : [-7846092427 / 10000000000, 14547832783 / 10000000000, 711770519 / 2500000000]
m : [-542426301 / 2000000000, 4963881243 / 5000000000, 10078770789 / 10000000000]
h : [367184779 / 1000000000, -80564793 / 2000000000, 3107423841 / 10000000000]
a : [5814878547 / 5000000000, 28831989 / 125000000, 5547753001 / 5000000000]
k : [5441359597 / 5000000000, 4243782739 / 5000000000, 1251985409 / 10000000000]
o : [-2183116189 / 5000000000, 5289032683 / 10000000000, 1375534451 / 10000000000]
c : [18146989733 / 10000000000, 399838379 / 2000000000, 1758591547 / 5000000000]
f : [3047248657 / 10000000000, 833361791 / 2000000000, 15878824059 / 10000000000]
n : [-931217603 / 2500000000, -17637367 / 10000000000, 4913304891 / 5000000000]
i : [5646468471 / 5000000000, -371999579 / 10000000000, -3367564971 / 10000000000]
b : [5967146213 / 5000000000, -1419662973 / 2500000000, 1016701753 / 2000000000]
p : [346316217 / 1000000000, 1134561977 / 2000000000, -302062583 / 625000000]
l : [494724611 / 2500000000, 13006439329 / 10000000000, 900673309 / 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 = 124995710768255798292693927682901149409434876215980457288481 / 250001013985833604227854148384691523722100000000000000000000
Collision distance in [70709321 / 100000000, 35354661 / 50000000] ~ [0.70709, 0.70709]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1847 / 10000, 1849 / 10000] ~ [0.1847, 0.1849]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 324779811606347025670639318935989 / 5000000000000000000000000000000000000000
rho in [12743 / 50000000, 25487 / 100000000] ~ [0.00025, 0.00025]
sigma_min ^ 2 / (16 * E ^ .5) in [3411409 / 10733126304, 3418801 / 10733126288] ~ [0.00032, 0.00032]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [5101731 / 50000000, 2567237 / 25000000] ~ [0.10203, 0.10269]
LHS DEN := 8 * |E| ^ .5 in [670820393 / 12500000, 335410197 / 6250000] ~ [53.66563, 53.66563]
LHS := (LHS NUM) / (LHS DEN) in [1700577 / 894427192, 2567237 / 1341640786] ~ [0.0019, 0.00191]
CD / |V| ^ .5 in [1055363 / 6153889, 11784887 / 68718427] ~ [0.1715, 0.1715]
Success: LHS < CD / |V| ^ .5
Success: existence proven