show/hide visualization coordinates
a : (0.03846240660022193, 0.9266508295418108, 0.18617821652173505)
b : (0.5162497601680033, 0.2539381034743111, 0.7511355888068314)
c : (0.7315439873473643, 0.332651080054721, -0.22223605453192102)
d : (0.25375909820535136, 1.0053675350733302, -0.7871916565739828)
e : (-0.23709409131771675, 0.2033075853637204, -0.44694473122167466)
f : (-0.4522257210923054, 0.1245076362258637, 0.5264596255152134)
g : (-0.17682904914929737, 0.8479427248380105, 1.1595476374494744)
h : (0.30095270981653954, 0.17522658428583815, 1.7245069401418858)
i : (0.02831401859614302, -0.5496739585187682, 1.09190331909298)
j : (0.24538646439590706, -0.4719078708616193, 0.11884980199689277)
k : (0.45890292554270895, -0.39224873009978867, -0.8548372023503792)
l : (0.9468368229065608, 0.4113648475578511, -1.1956080992557907)
m : (0.46905458038005354, 1.0840840217010568, -1.7605621034342613)
n : (-0.018879199311187977, 0.28046720251910806, -1.4197951834463631)
o : (-0.5068124726842946, -0.5231452186875672, -1.0790243872214358)
p : (-0.7221028641556307, -0.601854254328044, -0.10565174467906868)
q : (-0.9374009844239848, -0.6805686653616088, 0.8677165527633321)
r : (-0.6647629701555813, 0.04432965219535989, 1.5003179594990932)
s : (-0.2443248770243065, -1.2745755483220456, 0.45930336646690995)
t : (-0.029030544644546685, -1.1958635566515379, -0.5140678455394703)
show/hide computer existence proof (failed)
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['m', 'l', 'd'], ['a', 'f', 'g'], ['p', 'f', 'q'], ['c', 'k', 'j'], ['e', 'n', 'o'], ['p', 'f', 'e'], ['e', 'n', 'd'], ['b', 'j', 'i'], ['a', 'c', 'b'], ['f', 'r', 'g'], ['c', 'l', 'd'], ['t', 'o', 'p'], ['n', 'l', 'm'], ['b', 'c', 'j'], ['h', 'r', 'i'], ['k', 'n', 'o'], ['q', 's', 'i'], ['p', 'q', 's'], ['a', 'e', 'd'], ['q', 'r', 'i'], ['t', 's', 'j'], ['h', 'g', 'r'], ['a', 'g', 'b'], ['j', 's', 'i'], ['a', 'c', 'd'], ['k', 't', 'o'], ['c', 'k', 'l'], ['b', 'h', 'g'], ['b', 'h', 'i'], ['f', 'q', 'r'], ['p', 'e', 'o'], ['t', 'k', 'j'], ['n', 'm', 'd'], ['p', 't', 's'], ['k', 'n', 'l'], ['a', 'f', 'e']]
Coordinate Data:
b : [101208355656872527469 / 100000000000000000000, 87533631610205224063 / 100000000000000000000, 131048366422982788933 / 100000000000000000000]
k : [95473672194343085211 / 100000000000000000000, 22914948252795239573 / 100000000000000000000, -3693614086592283179 / 12500000000000000000]
m : [48244418839038772509 / 50000000000000000000, 170548223432879788421 / 100000000000000000000, -6006070140056324721 / 5000000000000000000]
a : [53429620300094377017 / 100000000000000000000, 38701226054238794017 / 25000000000000000000, 74552629194473149247 / 100000000000000000000]
f : [4360807530841647653 / 100000000000000000000, 74590584885360476353 / 100000000000000000000, 6786298130863811169 / 6250000000000000000]
j : [74122026079662899801 / 100000000000000000000, 2989806835322436179 / 20000000000000000000, 135639575483977853 / 200000000000000000]
t : [46680325175617518637 / 100000000000000000000, -57446534402379664511 / 100000000000000000000, 2264011494176307441 / 50000000000000000000]
l : [36066765482682064459 / 25000000000000000000, 103276306018559214647 / 100000000000000000000, -63626002383279414691 / 100000000000000000000]
g : [31900474725142450053 / 100000000000000000000, 146934093746575154427 / 100000000000000000000, 171889571287247084361 / 100000000000000000000]
i : [52414781499686489499 / 100000000000000000000, 7172425410897284987 / 100000000000000000000, 165125139451597667999 / 100000000000000000000]
p : [-11313453387745440979 / 50000000000000000000, 61074869686553639 / 3125000000000000000, 22684816537196388903 / 50000000000000000000]
s : [5030178387528308163 / 20000000000000000000, -65317733569430436333 / 100000000000000000000, 101865144188990642363 / 100000000000000000000]
h : [39839325310863074097 / 50000000000000000000, 19915619922839479827 / 25000000000000000000, 228385501556488240909 / 100000000000000000000]
q : [-5519589850290786049 / 12500000000000000000, -184907664793336631 / 3125000000000000000, 71353231409316432929 / 50000000000000000000]
n : [381563677671627139 / 800000000000000000, 45093270757342455881 / 50000000000000000000, -2688897212573020807 / 3125000000000000000]
o : [-1097867628357276651 / 100000000000000000000, 4912649697008691977 / 50000000000000000000, -5196763117984393817 / 10000000000000000000]
e : [25873970508300514419 / 100000000000000000000, 41235289899573072311 / 50000000000000000000, 11240334420132177693 / 100000000000000000000]
d : [74959289460607322743 / 100000000000000000000, 40669143692526784103 / 25000000000000000000, -5696089528774658257 / 25000000000000000000]
r : [-8446458687742972217 / 50000000000000000000, 66572786482310096877 / 100000000000000000000, 51491650873052237847 / 25000000000000000000]
c : [7671111148425537867 / 6250000000000000000, 23851232317061552127 / 25000000000000000000, 4213900261138442883 / 12500000000000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 13888893406798457277400547679607044178794155379655944010722743729839250547662002154071902354908229387195115660716136489 / 27777815974977823880811178918602102471096888917167224076910127676266440108838815000000000000000000000000000000000000000
Collision distance in [70710641 / 100000000, 35355321 / 50000000] ~ [0.70711, 0.70711]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [33 / 5000, 17 / 2500] ~ [0.0066, 0.0068]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 8693431691915514554031734528856469449238214048697266769686448016033673 / 20000000000000000000000000000000000000000000000000000000000000000000000000000000
rho in [208487789 / 10000000000000, 208587789 / 10000000000000] ~ [2e-05, 2e-05]
sigma_min ^ 2 / (16 * E ^ .5) in [1089 / 2939387692, 289 / 734846922] ~ [0.0, 0.0]
Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)