Drawing polygon from lines

I have polygon as shown in Fig1. I also know the coordinates of the vertices. I now want to use those vertices to create a serie of lines that reproduce the same polygon. I have the following code, but can't reproduce the initial figure (see Fig2). I know the "patch" function can be used but it doesn't serve my goal.

clear all
Vertex_X=[30;43;49;45;22;19;30;43;89;28;30;28;0;19;54;45;49;89;54;89;96;66];%X coordinate of vertex
Vertex_Y=[38;40;55;69;66;41;38;40;0;16;38;16;19;41;86;69;55;44;86;44;40;100];%Y coordinate of vertex
 
for i=1:(length(Vertex_X)-1)
    X1(i)=Vertex_X(i);
    Y1(i)=Vertex_Y(i);
    X2(i)=Vertex_X(i+1);
    Y2(i)=Vertex_Y(i+1);
end
A=[X1 Y1];
B=[X2 Y2];
plot(A.',B.','LineWidth', 0.75)

[Bruno Luong]

Not smart. A polygon is a set of vertexes and connectivity list.

If you throw away the connectivity list then there is no reliable way to bring them back.

So try to make the connectivity of those Voronoi's diagram available instead of asking such request.

[VBBV]

@ Bruno

You are right ! thats why it does not resemble