Gutman and Trinajstic deducted that total π-energy of a chemical molecule depends upon a numeric value which is termed as zagreb index. In that same report, they also defined a term for a particular atom with respect to other atom which is away from at a distance two. This quantity provides π-energy for a molecule. Now a days, in subject context, this quantity is termed as connection number. In this paper, we have discovered a new graph. It is composed of p-sided polygon in two dimensional rhombohedral plane. This 2D network astonishingly a new discovery in literature, its topological properties are explained via different connection numbers.