show/hide visualization coordinates
a : (-1.0295424824368422, -0.5619206567578947, -0.15030395923157902)
b : (-1.009531218236842, 0.15864482474210528, -0.843402030131579)
c : (-0.2099402494368422, -0.4261873847578947, -0.7069265048315789)
d : (-0.2690263205368422, -1.2080793708578947, -0.086318933031579)
e : (-0.6437374482368422, -0.7931992542578947, 0.7428167973684211)
f : (-0.9782448942368422, 0.13269473574210533, 0.567246048668421)
g : (-1.7015529874368422, 0.17807167794210532, -0.12178685003157902)
h : (-0.9641670174368422, 0.8535318896421054, -0.12571542993157903)
i : (-0.12988289873684222, 0.5643101660421053, -0.595098859131579)
j : (0.6818428309631579, 0.016884507942105276, -0.798633840031579)
k : (0.6203929944631579, -0.9126817490578947, -0.435136259231579)
l : (0.25064242626315775, -0.5057147003578947, 0.40012557896842105)
m : (-0.17998476363684224, -0.007869472657894727, 1.152927247768421)
n : (-0.13888490753684224, 0.6502754288421053, 0.40115860616842103)
o : (0.7227403183631578, 0.7311048848421053, -0.09990882353157898)
p : (1.5569669343631578, 0.4436048855421053, -0.570450748931579)
q : (1.144336158263158, -0.21716779615789472, 0.056538330368420986)
r : (0.7058112880631577, 0.2909294330421053, 0.7978433580684211)
s : (1.5717622371631579, 0.6127679505421053, 0.415026270668421)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['m', 'f', 'e'], ['k', 'd', 'c'], ['l', 'k', 'q'], ['j', 'i', 'o'], ['m', 'l', 'e'], ['b', 'i', 'c'], ['p', 'q', 's'], ['k', 'l', 'd'], ['b', 'g', 'a'], ['j', 'i', 'c'], ['a', 'f', 'e'], ['b', 'a', 'c'], ['b', 'h', 'i'], ['n', 'i', 'o'], ['j', 'o', 'p'], ['m', 'l', 'r'], ['a', 'd', 'e'], ['b', 'g', 'h'], ['m', 'n', 'r'], ['n', 'o', 'r'], ['g', 'h', 'f'], ['j', 'q', 'p'], ['j', 'k', 'q'], ['g', 'a', 'f'], ['a', 'd', 'c'], ['l', 'd', 'e'], ['q', 'l', 'r'], ['p', 'o', 's'], ['j', 'k', 'c'], ['n', 'f', 'h'], ['r', 'q', 's'], ['m', 'n', 'f'], ['s', 'o', 'r'], ['h', 'i', 'n']]
Coordinate Data:
n : [1703775141 / 5000000000, 10622349543 / 10000000000, 4082264969 / 5000000000]
d : [263267019 / 1250000000, -3980599227 / 5000000000, 1644877273 / 5000000000]
s : [20514021729 / 10000000000, 256181869 / 250000000, 8303206583 / 10000000000]
k : [5500164651 / 5000000000, -1251805559 / 2500000000, -49604679 / 2500000000]
q : [811988047 / 500000000, 1947917293 / 10000000000, 235916359 / 500000000]
l : [365141181 / 500000000, -937551749 / 10000000000, 4077099833 / 5000000000]
o : [12023802541 / 10000000000, 11430644103 / 10000000000, 3153855641 / 10000000000]
g : [-12219130517 / 10000000000, 2950156017 / 5000000000, 183442211 / 625000000]
c : [2696996863 / 10000000000, -142278593 / 10000000000, -729080293 / 2500000000]
r : [5927256119 / 5000000000, 1405777917 / 2000000000, 12131377457 / 10000000000]
b : [-211956513 / 400000000, 2853021751 / 5000000000, -171243057 / 400000000]
a : [-5499025467 / 10000000000, -1499611313 / 10000000000, 662476071 / 2500000000]
h : [-4845270817 / 10000000000, 12654914151 / 10000000000, 2895789577 / 10000000000]
p : [20366068701 / 10000000000, 855564411 / 1000000000, -1551563613 / 10000000000]
e : [-13127801 / 80000000, -476549661 / 1250000000, 231622237 / 200000000]
j : [11614827667 / 10000000000, 2144220167 / 5000000000, -958348631 / 2500000000]
m : [2996551721 / 10000000000, 252556283 / 625000000, 7841108177 / 5000000000]
i : [349757037 / 1000000000, 1952539383 / 2000000000, -359608943 / 2000000000]
f : [-997209917 / 2000000000, 1361635653 / 2500000000, 9825404363 / 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 = 1420618070311450965088039216921663552673645539207005929087 / 2710400786798003737507823669219485461012500000000000000000
Collision distance in [72397223 / 100000000, 9049653 / 12500000] ~ [0.72397, 0.72397]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [823 / 5000, 103 / 625] ~ [0.1646, 0.1648]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 14891483699407931024873 / 10000000000000000000000000000000000000000
rho in [122030667 / 100000000000000000, 1122030667 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [677329 / 2856571372, 84872 / 357071421] ~ [0.00024, 0.00024]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-9979 / 50000000, 2039 / 10000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [357071421 / 6250000, 714142843 / 12500000] ~ [57.13143, 57.13143]
LHS := (LHS NUM) / (LHS DEN) in [-9979 / 2856571368, 10195 / 2856571368] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [72397223 / 435889895, 1248228 / 7515343] ~ [0.16609, 0.16609]
Success: LHS < CD / |V| ^ .5
Success: existence proven