How to render perfect wireframed rectangle in 2D mode with OpenGL?

Question

Edit: just so you know: I have not solved this problem perfectly yet, currently I am using 0.5px offset, it seems to work, but as others have said,

Answer 1

This is not a bug, this is exactly following the specification. The last pixel of a line is not drawn to prevent overdraw with following line segments, which would cause problems with blending. Solution: Send the last vertex twice.

Code Update

// don't use glPolygonMode, it doesn't
// do what you think it does
glBegin(GL_LINE_STRIP);
    glVertex2f(a);
    glVertex2f(b);
    glVertex2f(c);
    glVertex2f(d);
    glVertex2f(a);
    glVertex2f(a); // resend last vertex another time, to close the loop
glEnd();

BTW: You should learn how to use vertex arrays. Immediate mode (glBegin, glEnd, glVertex calls) have been removed from OpenGL-3.x core and onward.