show/hide visualization coordinates
a : (0.23625026611875, 0.7943984022437501, -0.6257129515187501)
b : (0.58589139991875, -0.14248499055624997, -0.62494719331875)
c : (0.00330290331875005, 0.17316749194375003, -1.3739159203187499)
d : (-0.72183855958125, 0.5877278206437501, -0.82408904551875)
e : (-0.38387356258124994, 0.5381575108437501, 0.11576330618124997)
f : (0.54958869731875, 0.8307400730437501, 0.32323294408125003)
g : (1.19671696371875, 0.6193333106437501, -0.40925063101875003)
h : (0.98833660351875, -0.06715508665624992, 0.28739225118125)
i : (0.18651910841875008, -0.64648400845625, 0.14087704518125)
j : (-0.39569584358125, -0.33285160955625, -0.60922992661875)
k : (-1.20466582308125, 0.03137561234375008, -0.14781243371875002)
l : (-0.8469492223812499, -0.04540800705624992, 0.78285566578125)
m : (0.14724307681875004, 0.05770323774375008, 0.81367362008125)
n : (0.7257220404187501, -0.74133316055625, 0.97769473048125)
o : (-0.26981730768124995, -0.82934188055625, 1.01169279778125)
p : (-0.7967307406812499, -0.8275447160562499, 0.16177574128124994)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['k', 'p', 'l'], ['o', 'n', 'i'], ['d', 'a', 'e'], ['a', 'g', 'b'], ['a', 'c', 'b'], ['a', 'f', 'g'], ['b', 'c', 'j'], ['m', 'h', 'n'], ['p', 'o', 'i'], ['o', 'm', 'n'], ['f', 'e', 'm'], ['p', 'j', 'k'], ['b', 'j', 'i'], ['d', 'j', 'k'], ['h', 'n', 'i'], ['d', 'a', 'c'], ['b', 'g', 'h'], ['d', 'e', 'k'], ['k', 'e', 'l'], ['a', 'e', 'f'], ['e', 'm', 'l'], ['d', 'c', 'j'], ['g', 'f', 'h'], ['p', 'j', 'i'], ['p', 'o', 'l'], ['f', 'm', 'h'], ['o', 'm', 'l'], ['b', 'h', 'i']]
Coordinate Data:
n : [261309797 / 200000000, -1626109511 / 10000000000, 1900034471 / 1250000000]
j : [185131101 / 1000000000, 2458705999 / 10000000000, -668970803 / 10000000000]
o : [3110096369 / 10000000000, -2506196711 / 10000000000, 15540256441 / 10000000000]
p : [-2159037961 / 10000000000, -1244112533 / 5000000000, 1760271469 / 2500000000]
k : [-1247677757 / 2000000000, 3050489109 / 5000000000, 1972602063 / 5000000000]
e : [98476691 / 500000000, 11168797203 / 10000000000, 263238461 / 400000000]
g : [17775439083 / 10000000000, 11980555201 / 10000000000, 1330822153 / 10000000000]
b : [2333436689 / 2000000000, 4362372189 / 10000000000, -82614347 / 1000000000]
l : [-1330611389 / 5000000000, 666642753 / 1250000000, 13251885121 / 10000000000]
m : [3640350107 / 5000000000, 795531809 / 1250000000, 1695008083 / 1250000000]
d : [-28202323 / 200000000, 11664500301 / 10000000000, -352195249 / 1250000000]
c : [5841298479 / 10000000000, 3759448507 / 5000000000, -415791537 / 500000000]
a : [8170772107 / 10000000000, 13731206117 / 10000000000, -208450263 / 2500000000]
i : [767346053 / 1000000000, -67761799 / 1000000000, 1366419783 / 2000000000]
h : [15691635481 / 10000000000, 1278917807 / 2500000000, 331890039 / 400000000]
f : [11304156419 / 10000000000, 563784913 / 400000000, 540978619 / 625000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 16
|E| = 42
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 486896315840186129441728881334909743452176050450710940630841 / 999376939292987595162169061275890313829100000000000000000000
Collision distance in [8724963 / 12500000, 13959941 / 20000000] ~ [0.698, 0.698]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [519 / 1000, 649 / 1250] ~ [0.519, 0.5192]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 1224251709064366728983229 / 10000000000000000000000000000000000000000
rho in [27661477 / 2500000000000000, 52661477 / 2500000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [149645 / 57606584, 1684804 / 648074069] ~ [0.0026, 0.0026]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-1989 / 10000000, 20211 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [648074069 / 12500000, 64807407 / 1250000] ~ [51.84593, 51.84593]
LHS := (LHS NUM) / (LHS DEN) in [-9945 / 2592296276, 20211 / 5184592552] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [69799704 / 400000001, 13959941 / 80000000] ~ [0.1745, 0.1745]
Success: LHS < CD / |V| ^ .5
Success: existence proven