A GL_TRIANGLE_FAN is a set of triangles with 1 common point, the the case on a 6 vertex polygon it would be something like:
glBegin(GL_TRIANGLE_FAN); // Draw A 6 vertex polygon
glVertex3f(-0.5f, 1.0f, 0.0f); // Top Left
glVertex3f(-1.0f, 0.0f, 0.0f); // Left
glVertex3f(-0.5f, 1.0f, 0.0f); // Bottom Left
glVertex3f(0.5f, 1.0f, 0.0f); // Top Right
glVertex3f(1.0f, 0.0f, 0.0f); // Right
glVertex3f(0.5f, 1.0f, 0.0f); // Bottom Right
glEnd();
if you want to draw the outline of a polygon you can use GL_LINE_LOOP:
glBegin(GL_LINE_LOOP); // Draw A 6 vertex polygon
glVertex3f(-0.5f, 1.0f, 0.0f); // Top Left
glVertex3f(-1.0f, 0.0f, 0.0f); // Left
glVertex3f(-0.5f, 1.0f, 0.0f); // Bottom Left
glVertex3f(0.5f, 1.0f, 0.0f); // Top Right
glVertex3f(1.0f, 0.0f, 0.0f); // Right
glVertex3f(0.5f, 1.0f, 0.0f); // Bottom Right
glEnd();
This questions you are asking are the very basic about OpenGL primitives, you should read some introduction to OpenGL either online or on paper, to learn all sorts of primitives you can use.
If you like reading online check this 2 links:
http://www.graphics.cornell.edu/~spf/opengl/
http://fly.cc.fer.hr/~unreal/theredbook/