specify all triangle that can be created with n point(without repeat triangle)

I have for example 20 points. I want to specify all triangle that can be created with these point and one vertex is common between all. these triangle are no repeat. I don't want delaunay triangle. I Sort the points by increasing angle around the common vertex and form the triangles v, P[i], P[i+1]. Then v,P[i],P[i+2],..then v,P[i],P[i+3],....but I don't know where termination it if the number of point is change. if suppose v is common vertex: v,1,2 is same with v,2,1 .can any body help me to write matlab code?