15 vertices

bcdefg aghijc abjkd ackle adlmf aemng afnihb bgi bhgnoj biokc cjold dkome elonf fmoig inmlkj

show/hide visualization coordinates

a : (-0.43790526092666676, -0.024408393139999984, 0.1517787727)
b : (-0.20792952432666673, 0.94793204446, 0.2008904251)
c : (-0.6907617747266666, 0.58868251256, -0.5972291577000002)
d : (-0.8859737794266667, -0.38935835393999996, -0.6648586439000002)
e : (-0.5983207144266667, -1.00811127584, 0.06560903800000001)
f : (-0.1154834358266667, -0.6488220231399999, 0.8637468665)
g : (0.0797197787733333, 0.32918896666, 0.9313677377)
h : (0.4084226255733333, 1.27352616416, 0.9179110398)
i : (0.7362326197733333, 0.6202371626600001, 0.23545119539999998)
j : (0.29139828307333326, 0.77005109946, -0.6470778108000002)
k : (-0.10007958422666668, -0.0020436312399999546, -1.1469336308)
l : (-0.0466958660266667, -0.92392296954, -0.7642223668000001)
m : (0.3981397138733333, -1.07373099974, 0.11831843650000001)
n : (0.7896010176733332, -0.30167541714, 0.6181645859)
o : (0.3796359011733333, -0.15754488623999996, -0.28291648760000004)
			
show/hide manual existence proof

This is the hexagonal antiprism with a tetrahedron attached.
			
show/hide computer existence proof (failed) (see shape-existence, preprint)

Attempting to prove existence

Starting realization:
	Abstract data:	
		mode: maximal_simplices
		data: [['a', 'd', 'e'], ['d', 'e', 'l'], ['o', 'i', 'n'], ['l', 'd', 'k'], ['h', 'i', 'g'], ['b', 'h', 'i'], ['o', 'i', 'j'], ['b', 'h', 'g'], ['a', 'b', 'g'], ['c', 'd', 'k'], ['i', 'n', 'g'], ['f', 'n', 'g'], ['f', 'e', 'm'], ['f', 'n', 'm'], ['j', 'b', 'i'], ['a', 'b', 'c'], ['a', 'f', 'e'], ['a', 'c', 'd'], ['o', 'l', 'k'], ['o', 'l', 'm'], ['j', 'b', 'c'], ['o', 'n', 'm'], ['a', 'f', 'g'], ['j', 'k', 'o'], ['j', 'c', 'k'], ['e', 'l', 'm']]
	Coordinate Data:
		e : [5380025961 / 5000000000, 7748834641 / 5000000000, 495109411 / 1250000000]
		o : [490242883 / 5000000000, 3496002693 / 5000000000, 465383159 / 625000000]
		m : [795447639 / 10000000000, 16153866521 / 10000000000, 3433781303 / 10000000000]
		h : [346309261 / 5000000000, -3659352559 / 5000000000, -456214473 / 1000000000]
		g : [397964699 / 1000000000, 2124666857 / 10000000000, -4696711709 / 10000000000]
		l : [2621901719 / 5000000000, 14655786219 / 10000000000, 1532398667 / 1250000000]
		a : [9155897387 / 10000000000, 1132128091 / 2000000000, 3099177941 / 10000000000]
		d : [3409145643 / 2500000000, 9310140063 / 10000000000, 11265552107 / 10000000000]
		c : [467378501 / 400000000, -235134301 / 5000000000, 2117851449 / 2000000000]
		n : [-3119165399 / 10000000000, 1686662139 / 2000000000, -1564680191 / 10000000000]
		b : [6856140021 / 10000000000, -4062763921 / 10000000000, 2608061417 / 10000000000]
		j : [1862861947 / 10000000000, -2283954471 / 10000000000, 346491993 / 312500000]
		k : [288882031 / 500000000, 1359248209 / 2500000000, 2010787747 / 1250000000]
		i : [-129274071 / 500000000, -785815103 / 10000000000, 1131226857 / 5000000000]
		f : [185364973 / 312500000, 2380955351 / 2000000000, -4020502997 / 10000000000]

Desired square lengths:
	default : 1

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

Checking self-intersection:
	Square collision distance = 499809210488095351347743148876918803410212304502944176089329 / 1000037885827767790919255010114173642471000000000000000000000
	Collision distance in [35347923 / 50000000, 70695847 / 100000000] ~ [0.70696, 0.70696]
	Success: starting realization non-self-intersecting

Checking inequality 2:
	sigma_min in [1373 / 10000, 11 / 80] ~ [0.1373, 0.1375]
	Success: sigma_min > 0

Checking inequality 3:
	rho_squared = 151808489250863417696641415392173199 / 10000000000000000000000000000000000000000
	rho in [194813 / 50000000, 389627 / 100000000] ~ [0.0039, 0.0039]
	sigma_min ^ 2 / (16 * E ^ .5) in [1885129 / 9991996800, 171875 / 908363344] ~ [0.00019, 0.00019]
	Failed: unable to verify rho < sigma_min ^ 2 / (16 * E ^ .5)