show/hide visualization coordinates
a : (-1.2586789918894736, 0.14129038964210527, -0.027831240757894782)
b : (-1.0139843275894738, -0.7679735184578946, -0.36452645415789475)
c : (-0.9413113318894737, -0.5596931904578948, 0.6108390878421053)
d : (-0.5867119339894737, 0.37308382984210525, 0.6755406907421052)
e : (-0.5080852782894737, 0.7669818073421053, -0.24024434525789473)
f : (-0.7550930078894738, 0.04483018854210524, -0.8863745340578948)
g : (-0.15867850098947367, -0.7578373109578946, -0.8825507781578947)
h : (-0.14132234168947366, -0.8882268218578948, 0.10876014134210521)
i : (-0.023039094989473707, -0.39780920135789477, 0.9721833462421052)
j : (0.1472019048105263, 0.5165940823421052, 1.3394497843421052)
k : (0.26596966271052636, 0.8114307975421052, 0.39131185614210523)
l : (0.3789928689105263, 1.1006286106421053, -0.5592618546578947)
m : (-0.34391578828947367, 0.8937271261421053, -1.2184999369578948)
n : (0.2380861159105263, 0.15996728664210527, -0.8679713625578949)
o : (0.6824491820105263, -0.5848161649578948, -0.3701369768578948)
p : (0.7428540067105263, -0.9039399484578947, 0.5756490812421052)
q : (0.8324826930105262, 0.07472422114210525, 0.7605359161421053)
r : (0.9448176010105263, 0.36325024664210526, -0.19032348505789476)
s : (1.4979665624105263, -0.38621242995789473, 0.17345106444210523)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['i', 'q', 'p'], ['d', 'i', 'c'], ['h', 'p', 'o'], ['j', 'i', 'q'], ['d', 'a', 'c'], ['b', 'g', 'f'], ['h', 'i', 'c'], ['d', 'a', 'e'], ['l', 'r', 'n'], ['b', 'c', 'h'], ['l', 'k', 'e'], ['l', 'k', 'r'], ['d', 'k', 'e'], ['s', 'r', 'o'], ['m', 'n', 'f'], ['d', 'k', 'j'], ['s', 'p', 'o'], ['r', 'n', 'o'], ['k', 'r', 'q'], ['b', 'a', 'c'], ['g', 'n', 'o'], ['k', 'j', 'q'], ['g', 'n', 'f'], ['g', 'h', 'o'], ['d', 'i', 'j'], ['b', 'g', 'h'], ['i', 'h', 'p'], ['m', 'e', 'f'], ['a', 'e', 'f'], ['b', 'a', 'f'], ['l', 'm', 'e'], ['s', 'r', 'q'], ['l', 'm', 'n'], ['s', 'q', 'p']]
Coordinate Data:
d : [10552138171 / 10000000000, 133095349 / 5000000000, -1005334449 / 5000000000]
c : [281962643 / 200000000, 9593960901 / 10000000000, -1363652869 / 10000000000]
n : [288019709 / 1250000000, 239735613 / 1000000000, 2684890327 / 2000000000]
s : [-10294646793 / 10000000000, 491197081 / 625000000, 602045473 / 2000000000]
q : [-3639808099 / 10000000000, 649957357 / 2000000000, -89394411 / 312500000]
p : [-685880309 / 2500000000, 13036428481 / 10000000000, -1011752803 / 10000000000]
i : [4915409781 / 10000000000, 797512101 / 1000000000, -4977095453 / 10000000000]
m : [4062088357 / 5000000000, -988048453 / 2000000000, 16929737379 / 10000000000]
a : [13817447 / 8000000, 25841251 / 100000000, 5023050417 / 10000000000]
b : [14824862107 / 10000000000, 11676764181 / 10000000000, 8390002551 / 10000000000]
e : [4882935807 / 5000000000, -3672789077 / 10000000000, 3573590731 / 5000000000]
r : [-4763157179 / 10000000000, 36452653 / 1000000000, 332398643 / 500000000]
j : [3212999783 / 10000000000, -1168911827 / 10000000000, -4324879917 / 5000000000]
k : [506330551 / 2500000000, -4117278979 / 10000000000, 103952431 / 1250000000]
l : [447545071 / 5000000000, -700925711 / 1000000000, 2584339139 / 2500000000]
h : [762280281 / 1250000000, 2575859443 / 2000000000, 914284149 / 2500000000]
f : [1223594891 / 1000000000, 3548727111 / 10000000000, 272169667 / 200000000]
g : [6271803841 / 10000000000, 5787701053 / 5000000000, 13570245791 / 10000000000]
o : [-2139472989 / 10000000000, 4922595323 / 5000000000, 4223053889 / 5000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 19
|E| = 51
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 8661484889714489865615226628191218923914486534193515211401 / 15226799007752088033782844555431107601345312500000000000000
Collision distance in [75420927 / 100000000, 294613 / 390625] ~ [0.75421, 0.75421]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [1417 / 2500, 567 / 1000] ~ [0.5668, 0.567]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 7049366774983907051367 / 5000000000000000000000000000000000000000
rho in [14842261 / 12500000000000000, 139842261 / 12500000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [2007889 / 714142843, 382725 / 136027208] ~ [0.00281, 0.00281]
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, 20113 / 100000000] ~ [-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, 20113 / 5713142736] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [75420927 / 435889895, 3428224 / 19813177] ~ [0.17303, 0.17303]
Success: LHS < CD / |V| ^ .5
Success: existence proven