How do I love thee?  Let me plot the ways!

A heart is drawn on a coordinate plane by plotting the following points and connecting them:

·     The coordinates of the points are (n, n),
(n – 3, n + 3), (n – 6, n), (n – 9, n + 3),
(n – 12, n), (n – 12, n – 3), (n – 6, n – 9),
and (n, n –3).

·     The coordinates of one point are (2, 14).

·     All coordinates are positive integers.

What is the value of n?

This brainteaser was written by Julia Zurkovsky.