23 vertices

bcdefg aghic abijkd acklme admnof aeopqg afqrhb bgrsti bhtjc cituvk cjvwld dkwpom dlone emo enmlpf folwq fpwvrg gqvush hrut hsuji jtsrv jurqwk kvqpl

show/hide visualization coordinates

a : (-0.673913043478261, 0.2133685777439922, -0.7809967295830423)
b : (-0.17391304347826098, 1.079393981528431, -0.7809967295830423)
c : (0.326086956521739, 0.2133685777439922, -0.7809967295830423)
d : (-0.17391304347826098, -0.6526568260404464, -0.7809967295830423)
e : (-1.173913043478261, -0.6526568260404464, -0.7809967295830423)
f : (-0.673913043478261, -0.3639816914456335, 0.0354998513446837)
g : (-0.17391304347826098, 0.5020437123388053, 0.0354998513446837)
h : (0.326086956521739, 1.3680691161232437, 0.0354998513446837)
i : (0.826086956521739, 1.079393981528431, -0.7809967295830423)
j : (0.826086956521739, 0.5020437123388053, 0.0354998513446837)
k : (0.326086956521739, -0.3639816914456335, 0.0354998513446837)
l : (-0.17391304347826098, -1.2300070952300721, 0.0354998513446837)
m : (-0.673913043478261, -1.518682229824885, -0.7809967295830423)
n : (-1.673913043478261, -1.518682229824885, -0.7809967295830423)
o : (-1.173913043478261, -1.2300070952300721, 0.0354998513446837)
p : (-0.673913043478261, -0.9413319606352593, 0.8519964322724097)
q : (-0.17391304347826098, -0.07530655685082066, 0.8519964322724097)
r : (0.326086956521739, 0.7907188469336179, 0.8519964322724097)
s : (0.826086956521739, 1.6567442507180568, 0.8519964322724097)
t : (1.326086956521739, 1.3680691161232437, 0.0354998513446837)
u : (1.326086956521739, 0.7907188469336179, 0.8519964322724097)
v : (0.826086956521739, -0.07530655685082066, 0.8519964322724097)
w : (0.326086956521739, -0.9413319606352593, 0.8519964322724097)
			
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: [['b', 'i', 'c'], ['u', 'v', 'r'], ['d', 'l', 'k'], ['o', 'f', 'p'], ['m', 'o', 'n'], ['v', 'q', 'r'], ['q', 'g', 'r'], ['c', 'i', 'j'], ['b', 'g', 'a'], ['i', 'j', 't'], ['v', 'k', 'w'], ['u', 's', 'r'], ['e', 'f', 'o'], ['b', 'h', 'g'], ['b', 'c', 'a'], ['v', 'q', 'w'], ['v', 'j', 'k'], ['l', 'p', 'w'], ['o', 'l', 'p'], ['l', 'k', 'w'], ['h', 'i', 't'], ['d', 'e', 'a'], ['m', 'e', 'n'], ['u', 'j', 't'], ['c', 'j', 'k'], ['q', 'f', 'g'], ['w', 'q', 'p'], ['u', 'v', 'j'], ['m', 'o', 'l'], ['d', 'c', 'k'], ['e', 'f', 'a'], ['m', 'd', 'e'], ['h', 's', 'r'], ['h', 's', 't'], ['f', 'g', 'a'], ['q', 'f', 'p'], ['u', 's', 't'], ['d', 'c', 'a'], ['b', 'h', 'i'], ['e', 'n', 'o'], ['m', 'd', 'l'], ['h', 'g', 'r']]
	Coordinate Data:
		n : [378014829268946592304720243161 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 2182469634360857001509548829109 / 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -1214486236029074717036243131371 / 125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		r : [2, 2309401076758503058036595122007 / 1000000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		f : [199999999999999999999999999631 / 200000000000000000000000000000, 1154700538379251529018297562069 / 1000000000000000000000000000000, 163299316185545206546485605131 / 200000000000000000000000000000]
		j : [1250000000000000000000000000923 / 500000000000000000000000000000, 202072594216369017578202073069 / 100000000000000000000000000000, 204124145231931508183107006037 / 250000000000000000000000000000]
		m : [1, -990335375574447130476275856361 / 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -968127804125151270324386225663 / 250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		q : [3 / 2, 721687836487032205636435975627 / 500000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		d : [3 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, -69584730203936413384617185003 / 125000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		k : [2000000000000000000000000001831 / 1000000000000000000000000000000, 577350269189625764509148779973 / 500000000000000000000000000000, 408248290463863016366214012077 / 500000000000000000000000000000]
		e : [1 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 4444370057377585009464421916667 / 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		w : [2, 577350269189625764509148780501 / 1000000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		h : [2, 2886751345948128822545743902509 / 1000000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		v : [5 / 2, 721687836487032205636435975627 / 500000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		a : [1, 346410161513775458705489268301 / 200000000000000000000000000000, -5406779438809410488829373230591 / 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		g : [187499999999999999999999999769 / 125000000000000000000000000000, 2020725942163690175782020732823 / 1000000000000000000000000000000, 102062072615965754091553503207 / 125000000000000000000000000000]
		t : [3, 2886751345948128822545743902509 / 1000000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		c : [2, 346410161513775458705489268301 / 200000000000000000000000000000, -148638405151072063679714754323 / 156250000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		p : [1, 577350269189625764509148780501 / 1000000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		i : [5 / 2, 1299038105676657970145584756129 / 500000000000000000000000000000, -938847598661542062454692358779 / 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		o : [1 / 2, 1154700538379251529018297561 / 4000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		b : [3 / 2, 1299038105676657970145584756129 / 500000000000000000000000000000, -1817794771564349245914877490383 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		u : [3, 2309401076758503058036595122007 / 1000000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]
		l : [3 / 2, 1154700538379251529018297561 / 4000000000000000000000000000, 816496580927726032732428024901 / 1000000000000000000000000000000]
		s : [5 / 2, 79385662013573542620007957319 / 25000000000000000000000000000, 1632993161855452065464856049803 / 1000000000000000000000000000000]

Desired square lengths:
	default : 1

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

Checking self-intersection:
	Square collision distance = 499881264259633313338684664977296446669949614118537935937009745404899189656261152936214050324093543731758724777451983689 / 1000171278874482093410079493112006377574573988121299515879755508002182413641945690000000000000000000000000000000000000000
	Collision distance in [706962276095088431101699848791 / 1000000000000000000000000000000, 88370284511886053887712481099 / 125000000000000000000000000000] ~ [0.70696, 0.70696]
	Success: starting realization non-self-intersecting

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