a : (-0.12749069793138468, -0.2307498375518907, 0.3144596732073459)
b : (0.8640260467938481, -0.20030208773838531, 0.4408291382962779)
c : (0.29522964376113714, 0.5556278665406782, 0.7649238144999517)
d : (-0.696098422607421, 0.5260350796420538, 0.6368957758651528)
e : (-1.118629500451434, -0.2594911113537093, 0.18477215652361562)
f : (-0.5498334062173268, -1.0154216571437913, -0.13932279331356673)
g : (0.44149383829622385, -0.9858278007390103, -0.011294255828851518)
h : (1.4355782042240763, -0.8777637574839213, -0.0221768398213662)
i : (0.8595760866969003, -0.2598844999928105, -0.5573840735817945)
j : (0.7751303788405532, 0.6300752753809159, -0.10923445404411453)
k : (-0.12560762040211737, 1.0494263175314922, 0.003964613620016821)
l : (-0.25632834791666015, 1.3707838366693332, 0.9418566337554356)
m : (-0.941900649443047, 0.5788169892350001, -0.33098647749325744)
n : (-0.8574538902746928, -0.3111430174225086, -0.7791362316215289)
o : (0.04328352545733766, -0.7304944294789492, -0.8923354570307229)
p : (-0.04097518882599327, 0.16031283390550266, -0.4458312230325952)
			

This is the hexagonal antiprism with two tetrahdera attached.
			

Attempting to prove existence

Starting realization:
	Abstract data:	
		mode: maximal_simplices
		data: [['e', 'f', 'n'], ['p', 'o', 'i'], ['i', 'b', 'h'], ['a', 'g', 'f'], ['d', 'a', 'c'], ['b', 'j', 'c'], ['k', 'j', 'p'], ['m', 'n', 'p'], ['m', 'e', 'n'], ['d', 'k', 'l'], ['b', 'h', 'g'], ['i', 'o', 'g'], ['b', 'j', 'i'], ['d', 'e', 'a'], ['d', 'm', 'e'], ['o', 'g', 'f'], ['i', 'h', 'g'], ['o', 'n', 'f'], ['b', 'a', 'g'], ['l', 'd', 'c'], ['k', 'j', 'c'], ['l', 'k', 'c'], ['p', 'o', 'n'], ['b', 'a', 'c'], ['m', 'k', 'p'], ['p', 'j', 'i'], ['d', 'm', 'k'], ['e', 'a', 'f']]
	Coordinate Data:
		i : [-17945077205528236279 / 50000000000000000000, 90419556859581197683 / 100000000000000000000, 102307050883644325569 / 100000000000000000000]
		e : [161930404303776963627 / 100000000000000000000, 45190108997835535811 / 50000000000000000000, 28091427873103311511 / 100000000000000000000]
		l : [378501445251497871 / 500000000000000000, -14529455361326635063 / 20000000000000000000, -47617019850078681841 / 100000000000000000000]
		g : [5918070429011173023 / 100000000000000000000, 163013886934201190379 / 100000000000000000000, 5962258638543753509 / 12500000000000000000]
		k : [501025730390762363 / 800000000000000000, -20255762446424533351 / 50000000000000000000, 9234436432692638247 / 20000000000000000000]
		m : [144257519202938263207 / 100000000000000000000, 1309881587360026971 / 20000000000000000000, 79667291274790616167 / 100000000000000000000]
		f : [21010158976073248087 / 20000000000000000000, 16597327257467926443 / 10000000000000000000, 12100184571364309753 / 20000000000000000000]
		b : [-7267030084150249679 / 20000000000000000000, 84461315634138681221 / 100000000000000000000, 621432423959271423 / 25000000000000000000]
		o : [22869550856449895343 / 50000000000000000000, 137480549808195072099 / 100000000000000000000, 4243818413391786829 / 3125000000000000000]
		c : [5136122470629962089 / 25000000000000000000, 8868320206232327283 / 100000000000000000000, -7480934481132572563 / 25000000000000000000]
		j : [-13722791812710880307 / 50000000000000000000, 1423579322208557091 / 100000000000000000000, 57492088929876331129 / 100000000000000000000]
		d : [59838648259687836231 / 50000000000000000000, 11827598896094771527 / 100000000000000000000, -8560467030525198141 / 50000000000000000000]
		a : [7852065506471503269 / 12500000000000000000, 87506090615489221277 / 100000000000000000000, 15122676204730281107 / 100000000000000000000]
		p : [13541243285308220349 / 25000000000000000000, 24199911734874940067 / 50000000000000000000, 91151765828724390927 / 100000000000000000000]
		n : [27162568657220569159 / 20000000000000000000, 47772704301275502871 / 50000000000000000000, 124482266687617760111 / 100000000000000000000]
		h : [-46745183081887040159 / 50000000000000000000, 76103741304346136193 / 50000000000000000000, 48786327507601496027 / 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 = 2551017949314804591829370382165458528586573558592201454783047462972988991074345006058038555965213574415832049700208009 / 5102044366279617788827087318549624176811673711110905720473045312995992228876655000000000000000000000000000000000000000
	Collision distance in [70710619 / 100000000, 3535531 / 5000000] ~ [0.70711, 0.70711]
	Success: starting realization non-self-intersecting

Checking inequality 2:
	sigma_min in [63 / 10000, 13 / 2000] ~ [0.0063, 0.0065]
	Success: sigma_min > 0

Checking inequality 3:
	rho_squared = 2018024673058638401860975349398830847500583342388193892534177140271679 / 20000000000000000000000000000000000000000000000000000000000000000000000000000000
	rho in [50224803 / 5000000000000, 50274803 / 5000000000000] ~ [1e-05, 1e-05]
	sigma_min ^ 2 / (16 * E ^ .5) in [63 / 164590240, 4225 / 10369185104] ~ [0.0, 0.0]
	Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)