Connecting vertices while drawing a filled polygon using patch

I am attempting to draw multiple filled polygons using patch. If I increase the edge width, the polygons do not look closed anymore -- The end of the last edge is noticeably squared off. Is there a way to make the last vertex look connected with thick edges?

For a triangle, my code looks something like

patch('Faces',linspace(1,3,3),'Vertices',v,'FaceColor',[1,1,1],'linewidth',A);

in which A is an integer and v is a matrix of x and y coordinates for three vertices. I have also tried using [linspace(1,3,3),1] in lieu of linspace(1,3,3), and using XData and YData instead of Faces and Vertices.

Any advice would be greatly appreciated!