23 vertices

bcdefg aghijc abjkld aclme admnof aeopqg afqhb bgqi bhqprj birskc cjsnml ckmd dlkne emksto entupf fouriq fpihg ipuvsj jrvtnk nsvwuo otwvrp ruwts tvu

show/hide visualization coordinates

a : (-0.6521739130434783, 0.8785764965929088, 0.7099970268936747)
b : (0.34782608695652173, 0.8785764965929088, 0.7099970268936747)
c : (-0.15217391304347827, 1.1672516311877217, -0.10649955403405131)
d : (-1.1521739130434783, 1.1672516311877217, -0.10649955403405131)
e : (-0.6521739130434783, 0.30122622740328303, -0.10649955403405131)
f : (-0.15217391304347827, 0.012551092808470166, 0.7099970268936747)
g : (-0.15217391304347827, 0.589901361998096, 1.5264936078214006)
h : (0.8478260869565217, 0.589901361998096, 1.5264936078214006)
i : (0.8478260869565217, 0.012551092808470166, 0.7099970268936747)
j : (0.34782608695652173, 0.30122622740328303, -0.10649955403405131)
k : (-0.15217391304347827, 0.589901361998096, -0.9229961349617773)
l : (-0.6521739130434783, 1.4559267657825345, -0.9229961349617773)
m : (-1.1521739130434783, 0.589901361998096, -0.9229961349617773)
n : (-0.6521739130434783, -0.2761240417863427, -0.9229961349617773)
o : (-0.15217391304347827, -0.5647991763811555, -0.10649955403405131)
p : (0.34782608695652173, -0.8534743109759684, 0.7099970268936747)
q : (0.34782608695652173, -0.2761240417863427, 1.5264936078214006)
r : (0.8478260869565217, -0.5647991763811555, -0.10649955403405131)
s : (0.34782608695652173, -0.2761240417863427, -0.9229961349617773)
t : (-0.15217391304347827, -1.1421494455707812, -0.9229961349617773)
u : (0.34782608695652173, -1.430824580165594, -0.10649955403405131)
v : (0.8478260869565217, -1.1421494455707812, -0.9229961349617773)
w : (0.34782608695652173, -2.00817484935522, -0.9229961349617773)
			
show/hide manual existence proof

This is part of the standard sphere packing arrangement (link).
			
show/hide computer existence proof (failed) (see shape-existence, preprint)

Attempting to prove existence

Starting realization:
	Abstract data:	
		mode: maximal_simplices
		data: [['u', 'v', 'r'], ['v', 's', 'r'], ['o', 'f', 'p'], ['b', 'c', 'j'], ['o', 'n', 't'], ['b', 'g', 'a'], ['h', 'q', 'i'], ['e', 'f', 'o'], ['b', 'h', 'g'], ['i', 'q', 'p'], ['b', 'c', 'a'], ['u', 'o', 't'], ['b', 'i', 'j'], ['c', 'l', 'k'], ['d', 'c', 'l'], ['h', 'q', 'g'], ['s', 'n', 't'], ['d', 'e', 'a'], ['u', 'v', 'w'], ['s', 'n', 'k'], ['m', 'e', 'n'], ['m', 'n', 'k'], ['i', 'r', 'p'], ['v', 's', 't'], ['s', 'j', 'r'], ['c', 'j', 'k'], ['s', 'j', 'k'], ['q', 'f', 'g'], ['u', 'o', 'p'], ['e', 'f', 'a'], ['m', 'd', 'e'], ['w', 'u', 't'], ['f', 'g', 'a'], ['q', 'f', 'p'], ['d', 'c', 'a'], ['b', 'h', 'i'], ['w', 'v', 't'], ['u', 'r', 'p'], ['e', 'n', 'o'], ['i', 'j', 'r'], ['m', 'd', 'l'], ['m', 'l', 'k']]
	Coordinate Data:
		n : [8658252104656267162853058187 / 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 4998844183334939673667545931347 / 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 5989125687061879551875212142153 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		r : [3 / 2, -1154700538379251529018297561 / 4000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		f : [31249999999999999999999999933 / 62500000000000000000000000000, 2255274489021975642613862419 / 7812500000000000000000000000, 1632993161855452065464856050241 / 1000000000000000000000000000000]
		j : [1000000000000000000000000000571 / 1000000000000000000000000000000, 577350269189625764509148780831 / 1000000000000000000000000000000, 204124145231931508183107006167 / 250000000000000000000000000000]
		m : [-1 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 1623623921225802195516089933597 / 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		q : [1, 1052251144365953361996662493737 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 489897948556635619639456814941 / 200000000000000000000000000000]
		e : [-1057786444064534062458340055423 / 1000000000000000000000000000000000000000000000000000000000, 577350269189625764509148779891 / 1000000000000000000000000000000, 816496580927726032732428025333 / 1000000000000000000000000000000]
		k : [1 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, -1208797322310604756830620056279 / 200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		d : [-1 / 2, 721687836487032205636435975627 / 500000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		w : [1, -346410161513775458705489268301 / 200000000000000000000000000000, 4126643730000690372007186037653 / 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		h : [3 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 489897948556635619639456814941 / 200000000000000000000000000000]
		v : [3 / 2, -13531646934131853855683174543 / 15625000000000000000000000000, -814867187284126478403226048113 / 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		a : [1749597396380072738274054346981 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 1154700538379251529018297561003 / 1000000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		g : [1 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 489897948556635619639456814941 / 200000000000000000000000000000]
		t : [1 / 2, -13531646934131853855683174543 / 15625000000000000000000000000, 1555286000437029846598742955259 / 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		p : [1, -577350269189625764509148780501 / 1000000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		c : [1 / 2, 721687836487032205636435975627 / 500000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		i : [3 / 2, 1154700538379251529018297561 / 4000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		o : [499999999999999999999999998933 / 1000000000000000000000000000000, -144337567297406441127287195433 / 500000000000000000000000000000, 816496580927726032732428025337 / 1000000000000000000000000000000]
		b : [1, 1154700538379251529018297561003 / 1000000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		u : [1, -1154700538379251529018297561003 / 1000000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		l : [2031918193078507254430087932151 / 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 346410161513775458705489268301 / 200000000000000000000000000000, 527586523845410312177661116963 / 625000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		s : [1, -9730092717005191978374096694683 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 3187976202733045732648921330391 / 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]

Desired square lengths:
	default : 1

Checking inequality 1:
	 d  = 3
	|V| = 23
	|E| = 63
	Success: d|V| >= |E|

Checking self-intersection:
	Square collision distance = 499790175255072129774667486554318284420711150970188477642228286058489560633362790151314933260341995245488796729224665121 / 1000016780271234549659727925842582776955878093266997039063824042301196562710238770000000000000000000000000000000000000000
	Collision distance in [176738116428852560657189815451 / 250000000000000000000000000000, 141390493143082048525751852361 / 200000000000000000000000000000] ~ [0.70695, 0.70695]
	Success: starting realization non-self-intersecting

Checking inequality 2:
	sigma_min in [0, 1 / 5000] ~ [0.0, 0.0002]
	Failed: sigma_min not positive