a : (-0.7690178332588224, 0.6564160037992739, -0.47720855249904004)
b : (-0.28352479067098996, -0.20950632011985404, -0.35687532441199143)
c : (-0.7152551377984977, 0.23493576711108266, 0.428033669669568)
d : (-0.20535335352806444, 1.0734170882228145, 0.23580790111867556)
e : (0.22807133062170176, 0.6299803690192848, -0.5487338066032384)
f : (-0.3355931705392045, 0.2129791144988023, -1.2617501512081457)
g : (0.15159298250583153, -0.6519364974961208, -1.1410496171219564)
h : (0.2053543810436781, -1.073415412816139, -0.23580836718676723)
i : (-0.22807043569086777, -0.629979897752637, 0.5487334679987261)
j : (-0.661494327841007, -0.18654234830797445, 1.3332764209164465)
k : (-0.1515916409848495, 0.6519375044010898, 1.141050493474737)
l : (0.2835176392496943, 0.20950074600469393, 0.35687473781488854)
m : (0.71525680413226, -0.23493568227687056, -0.4280335546074646)
n : (0.6614951467026073, 0.18654341344645892, -1.333276645533223)
o : (0.769018053510135, -0.656415078900686, 0.47720915032342415)
p : (0.3355943525463946, -0.21297876883321898, 1.2617501778553635)
			

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

Attempting to prove existence

Starting realization:
	Abstract data:	
		mode: maximal_simplices
		data: [['e', 'f', 'n'], ['d', 'e', 'l'], ['p', 'o', 'i'], ['i', 'b', 'h'], ['d', 'a', 'c'], ['k', 'j', 'p'], ['d', 'k', 'c'], ['g', 'n', 'f'], ['m', 'e', 'n'], ['l', 'k', 'p'], ['b', 'g', 'f'], ['d', 'k', 'l'], ['i', 'j', 'c'], ['b', 'h', 'g'], ['l', 'm', 'o'], ['b', 'a', 'f'], ['d', 'e', 'a'], ['m', 'n', 'g'], ['l', 'o', 'p'], ['k', 'j', 'c'], ['m', 'o', 'h'], ['m', 'h', 'g'], ['c', 'b', 'i'], ['b', 'a', 'c'], ['p', 'j', 'i'], ['l', 'e', 'm'], ['i', 'o', 'h'], ['e', 'a', 'f']]
	Coordinate Data:
		i : [70826658615134947939 / 100000000000000000000, 29160731680898400747 / 25000000000000000000, 2986700948140080817 / 100000000000000000000]
		e : [6303120495969499427 / 25000000000000000000, -187061999071971601 / 2000000000000000000, 28183357102084133613 / 25000000000000000000]
		l : [9833925560539371581 / 50000000000000000000, 6538972469572101993 / 20000000000000000000, 11086286983261916923 / 50000000000000000000]
		g : [32860316795465020767 / 100000000000000000000, 29709646674485495507 / 25000000000000000000, 171965009460208340591 / 100000000000000000000]
		k : [63178779144533128391 / 100000000000000000000, -5774406745889534567 / 50000000000000000000, -14061250399865249427 / 25000000000000000000]
		m : [-23506065367177824909 / 100000000000000000000, 77138505176016957789 / 100000000000000000000, 25165850802189788859 / 25000000000000000000]
		f : [20394733024992157239 / 25000000000000000000, 8086756374612417999 / 25000000000000000000, 92017531434413626649 / 50000000000000000000]
		b : [76372094113147174281 / 100000000000000000000, 37297784480157651559 / 50000000000000000000, 11693447523651478959 / 12500000000000000000]
		o : [-180513689406033211 / 625000000000000000, 23857288967679701223 / 20000000000000000000, 10139132715670274051 / 100000000000000000000]
		n : [-3625979924842510431 / 20000000000000000000, 6998119120736801851 / 20000000000000000000, 95593856150667496191 / 50000000000000000000]
		c : [29886282206474482119 / 25000000000000000000, 1884460014826352361 / 6250000000000000000, 15056680781055883207 / 100000000000000000000]
		j : [114169047830148863483 / 100000000000000000000, 72299171779127349289 / 100000000000000000000, -37733797171815981907 / 50000000000000000000]
		a : [31230349592982600981 / 25000000000000000000, -5998331715798742923 / 50000000000000000000, 105580902997916696801 / 100000000000000000000]
		p : [3615044947852179989 / 25000000000000000000, 3747140691582589779 / 5000000000000000000, -6831497003752366619 / 10000000000000000000]
		d : [4284684399928413499 / 6250000000000000000, -53696771873951541293 / 100000000000000000000, 3427925763614513379 / 10000000000000000000]
		h : [1099367077667214623 / 4000000000000000000, 160986478229943817577 / 100000000000000000000, 40720442233344705357 / 50000000000000000000]

Desired square lengths:
	default : 1

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

Checking self-intersection:
	Square collision distance = 55645784553594765157906683446245686162219892286064562207411897016193436545453977179310610858090865470765176114076569569 / 111111039140376000143768908581372895176522355808474206686667548071992737303509930000000000000000000000000000000000000000
	Collision distance in [70768099 / 100000000, 707681 / 1000000] ~ [0.70768, 0.70768]
	Success: starting realization non-self-intersecting

Checking inequality 2:
	sigma_min in [17 / 2500, 7 / 1000] ~ [0.0068, 0.007]
	Success: sigma_min > 0

Checking inequality 3:
	rho_squared = 15831247511253462758462276906635398793509597991545229415206353233397471 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000
	rho in [25164457 / 2000000000000, 25184457 / 2000000000000] ~ [1e-05, 1e-05]
	sigma_min ^ 2 / (16 * E ^ .5) in [289 / 648074070, 1225 / 2592296276] ~ [0.0, 0.0]
	Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)