15 vertices

bcdefg aghijc abjed ace adcjkf aeklmg afmnhb bgnmi bhmloj biokec ejolf fkoim flihng gmh ilkj

show/hide visualization coordinates

a : (-0.14065844797333338, -0.35426984005999995, -0.8789967615066666)
b : (-0.038647418573333314, -0.67099539376, 0.06402209039333334)
c : (-0.9420190268733334, -0.65973719806, -0.36467903110666666)
d : (-1.0440091765733333, -0.34321402226, -1.3077602470066667)
e : (-0.8266109646733334, 0.30951836314000003, -0.5820098702066666)
f : (0.08833816052666665, 0.32144349924000004, -0.1778784997066667)
g : (0.7625091765266666, -0.36542609835999995, -0.4505477944066667)
h : (0.8648416921266666, -0.68202202486, 0.4924822140933333)
i : (0.17860375052666666, -0.018132744360000008, 0.7896769382933333)
j : (-0.7248328695733334, -0.0069936653599999565, 0.3610978380933333)
k : (-0.6094317564733333, 0.96217934244, 0.14339880129333332)
l : (0.29371788802666665, 0.95103525694, 0.5718399356933334)
m : (0.9796880578266667, 0.28723869424000004, 0.27487731489333334)
n : (1.6660236876266667, -0.37662343905999995, -0.022133795306666704)
o : (-0.5075127524733333, 0.64599927014, 1.0866108664933334)
			
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: [['g', 'f', 'm'], ['a', 'd', 'e'], ['b', 'h', 'i'], ['o', 'i', 'j'], ['h', 'n', 'm'], ['d', 'c', 'e'], ['b', 'h', 'g'], ['a', 'b', 'g'], ['j', 'e', 'k'], ['f', 'e', 'k'], ['f', 'l', 'm'], ['h', 'i', 'm'], ['o', 'i', 'l'], ['j', 'b', 'i'], ['a', 'b', 'c'], ['a', 'f', 'e'], ['a', 'c', 'd'], ['j', 'c', 'e'], ['o', 'l', 'k'], ['m', 'n', 'g'], ['l', 'f', 'k'], ['h', 'n', 'g'], ['j', 'b', 'c'], ['i', 'l', 'm'], ['a', 'f', 'g'], ['j', 'k', 'o']]
	Coordinate Data:
		m : [-4467497901 / 10000000000, 258564689 / 2000000000, 1156707641 / 5000000000]
		e : [3398873081 / 2500000000, 267506689 / 2500000000, 10882287133 / 10000000000]
		o : [5202255101 / 5000000000, -1147391157 / 5000000000, -2901960117 / 5000000000]
		h : [-829758561 / 2500000000, 2746357659 / 2500000000, 13736629 / 1000000000]
		g : [-71740909 / 312500000, 7819471371 / 10000000000, 76541331 / 80000000]
		a : [6735967157 / 10000000000, 1926977197 / 2500000000, 6926078023 / 5000000000]
		l : [2392203797 / 10000000000, -2672571091 / 5000000000, -328105463 / 5000000000]
		d : [15769474443 / 10000000000, 759735061 / 1000000000, 18139790901 / 10000000000]
		c : [7374786473 / 5000000000, 336330699 / 312500000, 4354489371 / 5000000000]
		n : [-11330854199 / 10000000000, 3965722389 / 5000000000, 330220399 / 625000000]
		b : [5715856863 / 10000000000, 435006573 / 400000000, 4421967527 / 10000000000]
		j : [12577711373 / 10000000000, 4235147041 / 10000000000, 29024201 / 200000000]
		k : [5711850121 / 5000000000, -5456583037 / 10000000000, 1814100209 / 5000000000]
		i : [885836293 / 2500000000, 4346537831 / 10000000000, -354322619 / 1250000000]
		f : [277875067 / 625000000, 190155079 / 2000000000, 1710243357 / 2500000000]

Desired square lengths:
	default : 1

Checking inequality 1:
	 d  = 3
	|V| = 15
	|E| = 39
	Success: d|V| >= |E|

Checking self-intersection:
	Square collision distance = 4998488493781848733546356599520580482064443433082179779289 / 10000468581128460874488288061158822013316000000000000000000
	Collision distance in [17674583 / 25000000, 70698333 / 100000000] ~ [0.70698, 0.70698]
	Success: starting realization non-self-intersecting

Checking inequality 2:
	sigma_min in [1269 / 10000, 1271 / 10000] ~ [0.1269, 0.1271]
	Success: sigma_min > 0

Checking inequality 3:
	rho_squared = 47869280484411504539145678782292883 / 10000000000000000000000000000000000000000
	rho in [21879 / 10000000, 218791 / 100000000] ~ [0.00219, 0.00219]
	sigma_min ^ 2 / (16 * E ^ .5) in [536787 / 3330665600, 1615441 / 9991996784] ~ [0.00016, 0.00016]
	Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)