22 vertices

bcdefg aghic abijd acjke adklf aelmng afnohb bgopqi bhqrjc cirkd djrsle ekstmf fltun fmuog gnuph houvq hpvsri iqskj krqvtl lsvum mtvpon putsq

show/hide visualization coordinates

a : (0.28867513459481287, -0.5000000000000002, 0.6433710704294877)
b : (1.1547005383792515, -2.220446049250313e-16, 0.6433710704294877)
c : (0.5773502691896257, -2.220446049250313e-16, 1.4598676513572137)
d : (-0.28867513459481287, -0.5000000000000002, 1.4598676513572137)
e : (-0.5773502691896257, -1.0000000000000002, 0.6433710704294877)
f : (0.0, -1.0000000000000002, -0.17312551049823832)
g : (0.8660254037844386, -0.5000000000000002, -0.17312551049823832)
h : (0.8660254037844386, 0.4999999999999998, -0.17312551049823832)
i : (0.28867513459481287, 0.4999999999999998, 0.6433710704294877)
j : (-0.28867513459481287, 0.4999999999999998, 1.4598676513572137)
k : (-0.5773502691896257, -2.220446049250313e-16, 0.6433710704294877)
l : (-0.8660254037844386, -0.5000000000000002, -0.17312551049823832)
m : (-0.5, -0.8660254037844388, -1.0287251876655905)
n : (0.5, -0.8660254037844388, -1.0287251876655905)
o : (1.0, -2.220446049250313e-16, -1.0287251876655905)
p : (0.5, 0.8660254037844384, -1.0287251876655905)
q : (0.0, 0.9999999999999998, -0.17312551049823832)
r : (-0.5773502691896257, 0.9999999999999998, 0.6433710704294877)
s : (-0.8660254037844386, 0.4999999999999998, -0.17312551049823832)
t : (-1.0, -2.220446049250313e-16, -1.0287251876655905)
u : (0.0, -2.220446049250313e-16, -1.0287251876655905)
v : (-0.5, 0.8660254037844384, -1.0287251876655905)
			
show/hide manual existence proof

This is a hexagonal antiprism 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: [['n', 'o', 'g'], ['d', 'a', 'e'], ['h', 'o', 'p'], ['n', 'o', 'u'], ['a', 'g', 'f'], ['b', 'i', 'h'], ['n', 'm', 'f'], ['r', 'j', 'k'], ['v', 't', 'u'], ['v', 's', 't'], ['r', 'q', 's'], ['l', 'e', 'f'], ['m', 'l', 't'], ['d', 'a', 'c'], ['d', 'j', 'k'], ['b', 'g', 'h'], ['b', 'a', 'c'], ['a', 'e', 'f'], ['l', 'e', 'k'], ['n', 'm', 'u'], ['h', 'q', 'i'], ['v', 'u', 'p'], ['r', 'q', 'i'], ['m', 't', 'u'], ['h', 'q', 'p'], ['d', 'j', 'c'], ['b', 'a', 'g'], ['b', 'c', 'i'], ['n', 'g', 'f'], ['d', 'e', 'k'], ['s', 'l', 't'], ['v', 'q', 's'], ['r', 's', 'k'], ['s', 'l', 'k'], ['v', 'q', 'p'], ['r', 'j', 'i'], ['o', 'p', 'u'], ['j', 'c', 'i'], ['m', 'l', 'f'], ['h', 'o', 'g']]
	Coordinate Data:
		m : [7305504580649577435708931856301 / 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -233940878691853041737903484783 / 625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -577339537603165833542351962349 / 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		s : [-5719146934131853855683174543 / 15625000000000000000000000000, 341506350946109661690930792523 / 250000000000000000000000000000, 171119935433470438593847153453 / 200000000000000000000000000000]
		b : [1654700538379251529018297561003 / 1000000000000000000000000000000, 433012701892219323381861584731 / 500000000000000000000000000000, 1672096258095078225701663791781 / 1000000000000000000000000000000]
		h : [21344146934131853855683174543 / 15625000000000000000000000000, 341506350946109661690930792523 / 250000000000000000000000000000, 171119935433470438593847153453 / 200000000000000000000000000000]
		p : [1, 346410161513775458705489268301 / 200000000000000000000000000000, 1336709639002773533049778639821 / 1000000000000000000000000000000000000000000000000000000000]
		r : [-77350269189625764509148780501 / 1000000000000000000000000000000, 933012701892219323381861584731 / 500000000000000000000000000000, 1672096258095078225701663792553 / 1000000000000000000000000000000]
		o : [3 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 26107610136772920567378489059 / 39062500000000000000000000000000000000000000000000000000]
		u : [1 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 2057688560180642965197019423527 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		g : [21344146934131853855683174543 / 15625000000000000000000000000, 91506350946109661690930792523 / 250000000000000000000000000000, 855599677167352192969235766493 / 1000000000000000000000000000000]
		d : [211324865405187117745425609749 / 1000000000000000000000000000000, 5719146934131853855683174513 / 15625000000000000000000000000, 2488592839022804258434091816297 / 1000000000000000000000000000000]
		a : [98584391824351610281821798823 / 125000000000000000000000000000, 91506350946109661690930792221 / 250000000000000000000000000000, 1672096258095078225701663791631 / 1000000000000000000000000000000]
		l : [-5719146934131853855683174543 / 15625000000000000000000000000, 91506350946109661690930792523 / 250000000000000000000000000000, 855599677167352192969235766493 / 1000000000000000000000000000000]
		e : [-77350269189625764509148780501 / 1000000000000000000000000000000, -133974596215561353236276830537 / 1000000000000000000000000000000, 1672096258095078225701663791009 / 1000000000000000000000000000000]
		k : [-7735026918962576450914878117 / 100000000000000000000000000000, 433012701892219323381861584731 / 500000000000000000000000000000, 1672096258095078225701663792017 / 1000000000000000000000000000000]
		i : [98584391824351610281821798823 / 125000000000000000000000000000, 34150635094610966169093079251 / 25000000000000000000000000000, 1672096258095078225701663792403 / 1000000000000000000000000000000]
		t : [-1 / 2, 13531646934131853855683174543 / 15625000000000000000000000000, 6683548195013867665248893199099 / 10000000000000000000000000000000000000000000000000000000000]
		c : [1077350269189625764509148780501 / 1000000000000000000000000000000, 13531646934131853855683174513 / 15625000000000000000000000000, 2488592839022804258434091816683 / 1000000000000000000000000000000]
		n : [1, -6368617337436978841632339043397 / 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 2295536447986580583845921066993 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]
		q : [1 / 2, 466506350946109661690930792523 / 250000000000000000000000000000, 855599677167352192969235767651 / 1000000000000000000000000000000]
		j : [211324865405187117745425609749 / 1000000000000000000000000000000, 21344146934131853855683174513 / 15625000000000000000000000000, 2488592839022804258434091817069 / 1000000000000000000000000000000]
		v : [311194833036258727295944628139 / 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 346410161513775458705489268301 / 200000000000000000000000000000, 1336709639002773533049778639821 / 1000000000000000000000000000000000000000000000000000000000]
		f : [1 / 2, -133974596215561353236276829907 / 1000000000000000000000000000000, 855599677167352192969235766107 / 1000000000000000000000000000000]

Desired square lengths:
	default : 1

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

Checking self-intersection:
	Square collision distance = 520940587964060882183607789504536636828400942210442682472695798790121393970422432154195385035957088546068113763248847809 / 998661468116206773976858932841263456044802312762836809923322193883398367832435310000000000000000000000000000000000000000
	Collision distance in [722245677144546297998918368071 / 1000000000000000000000000000000, 90280709643068287249864796009 / 125000000000000000000000000000] ~ [0.72225, 0.72225]
	Success: starting realization non-self-intersecting

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