a : (-0.7836344741380709, 0.1388068321142647, -0.6784696024521853)
b : (-0.23327886654301333, -0.6932680384152882, -0.7474158051885015)
c : (-0.6282395216075433, -0.4264442660454836, 0.1316811204281369)
d : (-1.1785959451409127, 0.4056342070668618, 0.2006273749444834)
e : (-1.3339904784792562, 0.9708871593822169, -0.6095222172659173)
f : (-0.4264412610190257, 0.9355831097064972, -0.1910627442170103)
g : (0.12472634765707846, 0.10418416211107334, -0.2617213932690393)
h : (0.6742700741122736, -0.7285742188535588, -0.32895649442276353)
i : (0.3170768171314439, -1.5253457622368924, -0.8163634363563744)
j : (-0.07788277776668917, -1.2585218871160788, 0.06273330785960624)
k : (0.27930974394550795, -0.4617483440937502, 0.5501396629231644)
l : (-0.2710465188570138, 0.370330198614306, 0.6190861688073643)
m : (0.48110595151130525, 0.9002790027060094, 0.22739539088009164)
n : (1.0314630167586074, 0.0681988632409386, 0.158448897447533)
o : (0.6365028589436798, 0.3350254769677482, 1.0375456684677287)
p : (1.388655033491628, 0.864973504851136, 0.6458541014136827)
			

This is part of the standard sphere packing arrangement (link).
			

Attempting to prove existence

Starting realization:
	Abstract data:	
		mode: maximal_simplices
		data: [['k', 'o', 'n'], ['i', 'b', 'h'], ['a', 'g', 'f'], ['d', 'a', 'c'], ['b', 'j', 'c'], ['m', 'n', 'p'], ['d', 'e', 'f'], ['h', 'n', 'g'], ['k', 'j', 'h'], ['b', 'h', 'g'], ['l', 'm', 'f'], ['l', 'm', 'o'], ['b', 'j', 'i'], ['d', 'e', 'a'], ['m', 'n', 'g'], ['b', 'a', 'g'], ['l', 'd', 'c'], ['i', 'j', 'h'], ['k', 'j', 'c'], ['k', 'n', 'h'], ['d', 'l', 'f'], ['l', 'k', 'c'], ['l', 'k', 'o'], ['p', 'o', 'n'], ['b', 'a', 'c'], ['m', 'p', 'o'], ['e', 'a', 'f'], ['m', 'g', 'f']]
	Coordinate Data:
		i : [2651118822548225411 / 20000000000000000000, 95892164213280466083 / 50000000000000000000, 16767646215798220431 / 12500000000000000000]
		e : [89181161836905565289 / 50000000000000000000, -57838963735350020791 / 100000000000000000000, 22691409563468008933 / 20000000000000000000]
		l : [72067927711586900287 / 100000000000000000000, 221673234144107121 / 10000000000000000000, -9403790789988106131 / 100000000000000000000]
		g : [4061330132522208881 / 12500000000000000000, 28831335991764336137 / 100000000000000000000, 78676965417652257623 / 100000000000000000000]
		k : [17032301431334724489 / 100000000000000000000, 85424586612246683807 / 100000000000000000000, -2509140201568116361 / 100000000000000000000]
		m : [-3147319325245008171 / 100000000000000000000, -12694537016932317039 / 25000000000000000000, 14882643501369578953 / 50000000000000000000]
		b : [68291162480186851777 / 100000000000000000000, 108576556044400480183 / 100000000000000000000, 127246406609598463269 / 100000000000000000000]
		f : [87607401927788086789 / 100000000000000000000, -54308558767778049083 / 100000000000000000000, 35805550256224676161 / 50000000000000000000]
		o : [-2335876258560306993 / 12500000000000000000, 5747204506096848701 / 100000000000000000000, -5124974075602454071 / 10000000000000000000]
		c : [5389361399331992071 / 5000000000000000000, 81894178807420024017 / 100000000000000000000, 245854462799591453 / 625000000000000000]
		j : [26375776801277217977 / 50000000000000000000, 82550970457239774291 / 50000000000000000000, 46231495304787702911 / 100000000000000000000]
		d : [162822870339976799793 / 100000000000000000000, -656834251907257267 / 50000000000000000000, 405526107453749811 / 1250000000000000000]
		a : [123326723239692613353 / 100000000000000000000, 25369068991445198057 / 100000000000000000000, 120351786335966854051 / 100000000000000000000]
		p : [-46951113761638654643 / 50000000000000000000, -5905949785280241929 / 12500000000000000000, -12080584050619944341 / 100000000000000000000]
		n : [-58183025849975228959 / 100000000000000000000, 16214932939388904593 / 50000000000000000000, 36659936345995023093 / 100000000000000000000]
		h : [-2807966448167729429 / 12500000000000000000, 22421434817645509837 / 20000000000000000000, 85400475533024672513 / 100000000000000000000]

Desired square lengths:
	default : 1

Checking inequality 1:
	 d  = 3
	|V| = 16
	|E| = 42
	Success: d|V| >= |E|

Checking self-intersection:
	Square collision distance = 499998917924649213538401197677140609352151051632332480374572508736563433559219413394726138521794408356268996992217565649 / 999998948455827188342498826750177594900770745317204053733552750438821860706377770000000000000000000000000000000000000000
	Collision distance in [35355319 / 50000000, 70710639 / 100000000] ~ [0.70711, 0.70711]
	Success: starting realization non-self-intersecting

Checking inequality 2:
	sigma_min in [71 / 10000, 73 / 10000] ~ [0.0071, 0.0073]
	Success: sigma_min > 0

Checking inequality 3:
	rho_squared = 38062815115387900440868264726020953537798508950590440386676858811001857 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
	rho in [195096937 / 10000000000000, 195196937 / 10000000000000] ~ [2e-05, 2e-05]
	sigma_min ^ 2 / (16 * E ^ .5) in [5041 / 10369185120, 5329 / 10369185104] ~ [0.0, 0.0]
	Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)