show/hide visualization coordinates
a : (-0.5300162875700001, 0.4998469303600001, 0.4856321473449999)
b : (-0.79262424867, 0.0429030760600001, -0.36421452865500015)
c : (-0.78302140697, -0.46756637203999996, 0.49562774054499986)
d : (-0.21361176667000004, -0.09208452863999983, 1.2269184123449999)
e : (-0.10478637477000008, 0.8994513357600001, 1.2977256396449999)
f : (0.41928973073, 0.8122345840600002, 0.45053175754499986)
g : (-0.13206017047000007, 0.7934242287600002, -0.38353026475500007)
h : (-0.36315104287, 0.30889906036000014, -1.2272318528550001)
i : (-1.0464081107699998, -0.4211380966399999, -1.2128955885550001)
j : (-0.94198311877, -0.94587250494, -0.36805878665500014)
k : (-0.045806722170000036, -0.99468551574, 0.0729459255449999)
l : (-0.22033571757000003, -1.0770239248399998, 1.054149276445)
m : (0.5409288862299999, -0.5171825928399999, 0.726958375145)
n : (0.70160569993, 0.3088595394600001, 1.2671781055449998)
o : (1.18751249923, 0.17376938666000014, 0.4036705880449999)
p : (0.85033840763, 0.6123410999600001, -0.42937712015500007)
q : (0.37306411952999996, 0.9856425811600001, -1.2248991236550002)
r : (0.59028344783, 0.010362110160000104, -1.184355738155)
s : (-0.13526046867000008, -0.5815496045399998, -0.8333193480550001)
t : (0.64604264483, -0.35063079253999985, -0.25345561665500016)
show/hide computer existence proof
(see shape-existence, preprint)
Attempting to prove existence
Starting realization:
Abstract data:
mode: maximal_simplices
data: [['h', 'q', 'g'], ['f', 'o', 'n'], ['i', 'j', 'b'], ['k', 'l', 'c'], ['p', 'q', 'g'], ['d', 'l', 'c'], ['k', 'm', 'l'], ['k', 'j', 'c'], ['k', 'm', 't'], ['o', 't', 'p'], ['h', 's', 'i'], ['k', 's', 't'], ['d', 'm', 'l'], ['d', 'c', 'a'], ['f', 'e', 'n'], ['b', 'a', 'g'], ['d', 'e', 'n'], ['p', 't', 'r'], ['d', 'e', 'a'], ['h', 'r', 's'], ['t', 'r', 's'], ['f', 'a', 'g'], ['f', 'e', 'a'], ['o', 't', 'm'], ['d', 'm', 'n'], ['k', 'j', 's'], ['c', 'a', 'b'], ['j', 'c', 'b'], ['f', 'p', 'g'], ['p', 'q', 'r'], ['j', 's', 'i'], ['o', 'm', 'n'], ['i', 'h', 'b'], ['f', 'o', 'p'], ['h', 'q', 'r'], ['g', 'h', 'b']]
Coordinate Data:
d : [6394594267 / 10000000000, 826143893 / 1250000000, -6779832307 / 10000000000]
s : [5611081287 / 10000000000, 11503801903 / 10000000000, 13822545297 / 10000000000]
k : [2358271911 / 5000000000, 3127032203 / 2000000000, 4759892561 / 10000000000]
r : [-822178939 / 5000000000, 1396171189 / 2500000000, 8666454599 / 5000000000]
n : [-2757580399 / 10000000000, 2599710463 / 10000000000, -7182429239 / 10000000000]
j : [3419576947 / 2500000000, 15147030907 / 10000000000, 9169939683 / 10000000000]
a : [2389659869 / 2500000000, 344918277 / 5000000000, 633030343 / 10000000000]
o : [-952081049 / 1250000000, 3950611991 / 10000000000, 90790371 / 625000000]
m : [-575406131 / 5000000000, 5430065893 / 5000000000, -356046387 / 2000000000]
b : [12184719087 / 10000000000, 5259275097 / 10000000000, 9131497103 / 10000000000]
q : [105567081 / 2000000000, -2084059977 / 5000000000, 17738343053 / 10000000000]
l : [403864611 / 625000000, 8229272553 / 5000000000, -1263035237 / 2500000000]
f : [65579293 / 10000000000, -2434039983 / 10000000000, 984034241 / 10000000000]
i : [3680639427 / 2500000000, 1237460853 / 1250000000, 8809153851 / 5000000000]
p : [-1061226869 / 2500000000, -217552571 / 5000000000, 4891561509 / 5000000000]
g : [1115815661 / 2000000000, -224593643 / 1000000000, 72848863 / 78125000]
e : [1326585087 / 2500000000, -1322483 / 4000000, -374395229 / 500000000]
t : [-275243731 / 1250000000, 9194613783 / 10000000000, 8023907983 / 10000000000]
h : [7889987029 / 10000000000, 1299657627 / 5000000000, 3552334069 / 2000000000]
c : [1208869067 / 1000000000, 5181984789 / 5000000000, 533074411 / 10000000000]
Desired square lengths:
default : 1
Checking inequality 1:
d = 3
|V| = 20
|E| = 54
Success: d|V| >= |E|
Checking self-intersection:
Square collision distance = 127522055292532568188792249579792745319106397586822741132121 / 249889079002610926763464384946307438936950000000000000000000
Collision distance in [7143631 / 10000000, 71436311 / 100000000] ~ [0.71436, 0.71436]
Success: starting realization non-self-intersecting
Checking inequality 2:
sigma_min in [5327 / 10000, 5329 / 10000] ~ [0.5327, 0.5329]
Success: sigma_min > 0
Checking inequality 3:
rho_squared = 3363837553333549844601 / 2500000000000000000000000000000000000000
rho in [115997199 / 100000000000000000, 1115997199 / 100000000000000000] ~ [0.0, 0.0]
sigma_min ^ 2 / (16 * E ^ .5) in [28376929 / 11757550768, 28398241 / 11757550752] ~ [0.00241, 0.00242]
Success: rho < sigma_min ^ 2 / (16 * E ^ .5)
Checking inequality 4:
LHS NUM := sigma_min - [sigma_min ^ 2 - 16 * rho * |E| ^ .5 ] ^ .5 in [-4997 / 25000000, 5031 / 25000000] ~ [-0.0002, 0.0002]
LHS DEN := 8 * |E| ^ .5 in [367423461 / 6250000, 734846923 / 12500000] ~ [58.78775, 58.78775]
LHS := (LHS NUM) / (LHS DEN) in [-4997 / 1469693844, 559 / 163299316] ~ [-0.0, 0.0]
CD / |V| ^ .5 in [35718155 / 223606798, 71436311 / 447213595] ~ [0.15974, 0.15974]
Success: LHS < CD / |V| ^ .5
Success: existence proven