show/hide visualization coordinates
a : (-0.6487758373692308, -0.6037015002615385, -0.02900574368461528)
b : (0.3126322635307692, -0.35511858076153846, -0.1469082261846153)
c : (-0.060629265669230825, -0.48738638146153845, 0.7713406832153847)
d : (-0.7145965692692308, 0.22732483243846152, 0.5233192199153848)
e : (-1.0477390294692308, 0.22593617043846154, -0.4195562610846153)
f : (-1.2376410635692308, -0.6636332920615384, -0.8350119009846153)
g : (-0.3255343452692308, -0.26078554706153845, -0.9110055092846152)
h : (0.5664091391307692, 0.1900107445384615, -0.9459271971846153)
i : (0.8937140476307691, 0.45139025453846154, -0.0378786034846153)
j : (0.9086832282307692, -0.27258459916153843, 0.6517853254153848)
k : (0.23722132713076916, 0.46563914653846156, 0.7163191670153847)
l : (-0.08767449786923082, 0.43058415793846155, -0.2287807486846153)
m : (1.203930602830769, 0.6523245943384615, 0.8913097950153847)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['d', 'l', 'e'], ['h', 'g', 'l'], ['c', 'a', 'd'], ['h', 'g', 'b'], ['a', 'g', 'b'], ['a', 'f', 'g'], ['i', 'h', 'l'], ['i', 'h', 'b'], ['c', 'k', 'd'], ['m', 'j', 'k'], ['k', 'd', 'l'], ['g', 'l', 'e'], ['a', 'f', 'e'], ['l', 'k', 'i'], ['c', 'j', 'b'], ['c', 'j', 'k'], ['m', 'j', 'i'], ['i', 'j', 'b'], ['a', 'd', 'e'], ['c', 'a', 'b'], ['m', 'k', 'i'], ['f', 'g', 'e']]
Coordinate Data:
g : [1940563749 / 10000000000, 661685763 / 10000000000, -3847625689 / 10000000000]
i : [7066523839 / 5000000000, 7783443779 / 10000000000, 4883643369 / 10000000000]
f : [-3590251717 / 5000000000, -3366791687 / 10000000000, -1543844803 / 5000000000]
m : [1723521323 / 1000000000, 9792787177 / 10000000000, 7087763677 / 5000000000]
e : [-5281483093 / 10000000000, 2764451469 / 5000000000, 1066866793 / 10000000000]
c : [917922909 / 2000000000, -1604322581 / 10000000000, 3243959059 / 2500000000]
l : [4319162223 / 10000000000, 7575382813 / 10000000000, 2974621917 / 10000000000]
j : [3570684871 / 2500000000, 271847621 / 5000000000, 5890141329 / 5000000000]
a : [-322962793 / 2500000000, -2767473769 / 10000000000, 4972371967 / 10000000000]
d : [-1950058491 / 10000000000, 2771394779 / 5000000000, 10495621603 / 10000000000]
b : [8322229837 / 10000000000, -140822287 / 5000000000, 1896673571 / 5000000000]
k : [7568120473 / 10000000000, 7925932699 / 10000000000, 6212810537 / 5000000000]
h : [10859998593 / 10000000000, 5169648679 / 10000000000, -524605321 / 1250000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 13
|E| = 33
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 434435292303962993573734545158833848402962359006613638077049 / 988365940575507856309305275205105416141000000000000000000000
Collision distance in [33149247 / 50000000, 13259699 / 20000000] ~ [0.66298, 0.66298]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [7121 / 10000, 7123 / 10000] ~ [0.7121, 0.7123]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 4296759584333946955989 / 5000000000000000000000000000000000000000
rho in [23175309 / 25000000000000000, 273175309 / 25000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [50708641 / 9191300240, 50737129 / 9191300224] ~ [0.00552, 0.00552]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-3999 / 20000000, 20071 / 100000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [71807033 / 1562500, 114891253 / 2500000] ~ [45.9565, 45.9565]
LHS := (LHS NUM) / (LHS DEN) in [-465 / 106875584, 20071 / 4595650112] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [33149247 / 180277564, 66298495 / 360555127] ~ [0.18388, 0.18388]
Success: LHS < CD / |V| ^ .5
Success: existence proven