Plot polygon that contains inside edges

Hi,

I have a set of vertices and set of edges that create this shape:

Vertices = [1 4; 2.8 6; 5 5.7;...
            7 4; 6 3.3; 4 1;...
            1.5 2.5; 3.8 2.5; 4 4;...
            1.7 3; 2 4.2; 4.2 4.1];

Edges = [1 2; 2 3; 3 4; 4 5; 5 6; 6 7; 7 1;...
             6 8; 8 9; 9 2;...
             7 10; 10 8;...
             1 11; 11 9;... 
             9 12; 12 3;...
             3 5];

How can I plot this shape and show the inside edges ? I know about the fill function and patch function but I don't know how to use them to show the edges inside.