How to order vertices of a flat convex polygon in 3d space along the edge?

I have a list of xyz-coordinates which build a flat polygon and i need to order them clockwise or counterclockwise. Its not important which direction it is though. I tried to use the atan2() function by calculating rays from the center of the polygon but it fails if the polygon is close to vertical. I would like to implement an approach which works without exceptions. Here is an example of 5 points.

-2.6055 1.1850 0.0880

-2.6320 1.1700 -0.0593

-2.3126 1.2170 -0.4326

-2.1860 1.2672 0.3596

-1.6203 1.4446 -0.0687

Thank you in advance!

[Jan von Kölln]

I found a way to give me a list of which lines build the vertices. So my goal is to isolate the different Points. How can i do that?

 233   291
 291   387
 388   387
 388   471
 233   471

I need to keep the order and isolate the nodes. In this case, it should be: 291, 387, 388, 471, 233

[Bruno Luong]

E = [...
 233   291;
 100  233;
 291   387;
 388   387;
 388   471;
 100   471 ]

n = size(E,1);
[u,~,L] = unique(E);
[~,is] = sort(L);
is(is) = flip(reshape(is+n*(2*(is <= n)-1),2,[]));
i = 1+n;
I = zeros(n,1);
for j=1:n
    I(j) = i;
    i = is(i);
end
V = u(L(I));

disp(V)

Answer 1

[Bruno Luong]

 xyz =[...
      -2.6055 1.1850 0.0880;
      -2.6320 1.1700 -0.0593;
      -2.3126 1.2170 -0.4326;
      -2.1860 1.2672 0.3596;
      -1.6203 1.4446 -0.0687 ];

xyzc = mean(xyz,1);
P = xyz - xyzc;
[~,~,V] = svd(P,0);

[~,is] = sort(atan2(P*V(:,1),P*V(:,2)));
xyz = xyz(is([1:end 1]),:);

close all
plot3(xyz(:,1),xyz(:,2),xyz(:,3))

[Jan von Kölln]

That works, thanks! If you know how to deal with my comment about the lines i would highly appreciate to get the answer. And thank you for your time!