22 vertices

bcdefg aghic abijkd acklme admnf aenog afohb bgopqi bhqrjc cirk cjrsld dksm dlstne emtpof fnphg hontuq hpuvri iqvskj krvtml msvupn ptvq qutsr

show/hide visualization coordinates

a : (0.2954545454545455, 0.8266606127033278, -0.11134044285378075)
b : (0.7954545454545455, 0.5379854781085149, -0.9278370237815068)
c : (-0.20454545454545447, 0.5379854781085149, -0.9278370237815068)
d : (-0.7045454545454545, 0.8266606127033278, -0.11134044285378075)
e : (-0.20454545454545447, 1.1153357472981407, 0.7051561380739453)
f : (0.7954545454545455, 1.1153357472981407, 0.7051561380739453)
g : (1.2954545454545454, 0.8266606127033278, -0.11134044285378075)
h : (0.7954545454545455, -0.03936479108111082, -0.11134044285378075)
i : (0.2954545454545455, -0.32803992567592366, -0.9278370237815068)
j : (-0.5378787878787878, -0.23181488081098608, -1.4721680777333241)
k : (-1.0378787878787878, 0.05686025378382678, -0.6556714968055981)
l : (-1.5378787878787878, 0.3455353883786397, 0.16082508412212793)
m : (-0.7045454545454545, 0.24931034351370204, 0.7051561380739453)
n : (0.2954545454545455, 0.24931034351370204, 0.7051561380739453)
o : (1.2954545454545454, 0.24931034351370204, 0.7051561380739453)
p : (0.7954545454545455, -0.6167150602707365, 0.7051561380739453)
q : (0.2954545454545455, -0.9053901948655494, -0.11134044285378075)
r : (-0.5378787878787878, -0.8091651500006118, -0.6556714968055981)
s : (-1.0378787878787878, -0.520490015405799, 0.16082508412212793)
t : (-0.20454545454545447, -0.6167150602707365, 0.7051561380739453)
u : (0.2954545454545455, -1.4827404640551751, 0.7051561380739453)
v : (-0.5378787878787878, -1.3865154191902376, 0.16082508412212793)
			
show/hide manual existence proof

This is shape 14_124 stacked on a truncated subdivided tetrahedron.
			
show/hide computer existence proof (failed) (see shape-existence, preprint)

Attempting to prove existence

Starting realization:
	Abstract data:	
		mode: maximal_simplices
		data: [['d', 'a', 'e'], ['h', 'o', 'p'], ['a', 'g', 'f'], ['b', 'i', 'h'], ['d', 'c', 'k'], ['d', 'l', 'k'], ['n', 'o', 'p'], ['r', 'j', 'k'], ['v', 't', 'u'], ['n', 't', 'p'], ['v', 's', 't'], ['n', 'e', 'f'], ['d', 'm', 'e'], ['q', 'u', 'p'], ['n', 'm', 't'], ['d', 'a', 'c'], ['m', 's', 'l'], ['m', 's', 't'], ['j', 'c', 'k'], ['b', 'g', 'h'], ['b', 'a', 'c'], ['a', 'e', 'f'], ['r', 's', 'v'], ['h', 'q', 'i'], ['r', 'q', 'i'], ['h', 'q', 'p'], ['n', 'o', 'f'], ['b', 'a', 'g'], ['d', 'm', 'l'], ['n', 'm', 'e'], ['b', 'c', 'i'], ['v', 'q', 'r'], ['o', 'g', 'f'], ['u', 't', 'p'], ['v', 'q', 'u'], ['r', 's', 'k'], ['s', 'l', 'k'], ['r', 'j', 'i'], ['j', 'c', 'i'], ['h', 'o', 'g']]
	Coordinate Data:
		m : [-55040461431968010369522330499 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -695698218655798684511405993869 / 2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -496277729587363066896726156803 / 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		s : [-333333333333333333333333333719 / 1000000000000000000000000000000, -769800358919501019345531707113 / 1000000000000000000000000000000, -13608276348795433878873800417 / 25000000000000000000000000000]
		b : [749999999999999999999999999421 / 500000000000000000000000000000, 288675134594812882254574390919 / 1000000000000000000000000000000, -408248290463863016366214012687 / 250000000000000000000000000000]
		h : [1499999999999999999999999999999 / 1000000000000000000000000000000, -1154700538379251529018297561 / 4000000000000000000000000000, -816496580927726032732428026319 / 1000000000000000000000000000000]
		p : [3 / 2, -13531646934131853855683174543 / 15625000000000000000000000000, -141718736001867038730542221483 / 100000000000000000000000000000000000000000000000000000000]
		r : [83333333333333333333333332851 / 500000000000000000000000000000, -105847549351431390160010609703 / 100000000000000000000000000000, -680413817439771693943690021027 / 500000000000000000000000000000]
		o : [2, 623933784603094858287799640673 / 2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -354296840004667596826355553707 / 250000000000000000000000000000000000000000000000000000000]
		u : [1, -346410161513775458705489268301 / 200000000000000000000000000000, -88574210001166899206588888427 / 62500000000000000000000000000000000000000000000000000000]
		g : [1999999999999999999999999999421 / 1000000000000000000000000000000, 115470053837925152901829756167 / 200000000000000000000000000000, -408248290463863016366214013041 / 500000000000000000000000000000]
		d : [-1157128633989234714530816917207 / 2000000000000000000000000000000000000000000000000000000000, 115470053837925152901829756167 / 200000000000000000000000000000, -163299316185545206546485604933 / 200000000000000000000000000000]
		a : [999999999999999999999999999421 / 1000000000000000000000000000000, 9021097956087902570455449711 / 15625000000000000000000000000, -81649658092772603273242802561 / 100000000000000000000000000000]
		l : [-833333333333333333333333333719 / 1000000000000000000000000000000, 96225044864937627418191463639 / 1000000000000000000000000000000, -544331053951817355154952015971 / 1000000000000000000000000000000]
		e : [1 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 588900723615016887168268072519 / 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		k : [-333333333333333333333333334297 / 1000000000000000000000000000000, -192450089729875254836382926277 / 1000000000000000000000000000000, -272165526975908677577476008269 / 200000000000000000000000000000]
		i : [499999999999999999999999999421 / 500000000000000000000000000000, -577350269189625764509148779833 / 1000000000000000000000000000000, -408248290463863016366214012687 / 250000000000000000000000000000]
		t : [1 / 2, -13531646934131853855683174543 / 15625000000000000000000000000, -3542968400046675968263555537077 / 5000000000000000000000000000000000000000000000000000000000]
		c : [249999999999999999999999999421 / 500000000000000000000000000000, 288675134594812882254574390919 / 1000000000000000000000000000000, -40824829046386301636621401251 / 25000000000000000000000000000]
		n : [1, 2204172672078762851338777846029 / 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 4858215092970255631020355625537 / 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		q : [999999999999999999999999999421 / 1000000000000000000000000000000, -1154700538379251529018297560669 / 1000000000000000000000000000000, -408248290463863016366214013041 / 500000000000000000000000000000]
		j : [166666666666666666666666665123 / 1000000000000000000000000000000, -240562612162344068545478658097 / 500000000000000000000000000000, -13608276348795433878873800417 / 6250000000000000000000000000]
		v : [4166666666666666666666666657 / 25000000000000000000000000000, -817912881351969833054627438933 / 500000000000000000000000000000, -136082763487954338788738004347 / 250000000000000000000000000000]
		f : [3 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, -354296840004667596826355553707 / 500000000000000000000000000000000000000000000000000000000]

Desired square lengths:
	default : 1

Checking inequality 1:
	 d  = 3
	|V| = 22
	|E| = 60
	Success: d|V| >= |E|

Checking self-intersection:
	Square collision distance = 2603760338826782666025555109389893600858715890321957612670656979914365599931310743042286252238549369900537280040178387 / 5208470027228603501893893314327711623388382685150188434730746138275976381959842968750000000000000000000000000000000000
	Collision distance in [707042335954969227971756271857 / 1000000000000000000000000000000, 353521167977484613985878135929 / 500000000000000000000000000000] ~ [0.70704, 0.70704]
	Success: starting realization non-self-intersecting

Checking inequality 2:
	sigma_min in [0, 1 / 5000] ~ [0.0, 0.0002]
	Failed: sigma_min not positive