3=3*(3- 1)/2

6=4*(4- 1)/2

10=5*(5- 1)/2

15=6*(6-5)/2

. . . .

Regular, with n points. For any point, all other points (N- 1) can form line segments, so a * * * has N*(N- 1) line segments.

But for any two points, the line segment formed by these two points is repeated once, so the actual line segment is only N*(N- 1)/2.