Explicit formulas for the ranks of Triangular numbers, Hexagonal numbers, Centered Hexagonal numbers, Centered Octagonal numbers, Centered Decagonal numbers and Centered Dodecagonal numbers satisfying the relations; 3,N 6,h 6,H t  t  ct , t 3,N  t6,h  ct 8,M , t 3,N  t6,h  ct10,M , 3,N 6,h 12,D t  t  ct are obtained.

Keywords : Equality of polygonal numbers, Centered Hexagonal numbers, Centered Octagonal numbers, Centered Decagonal numbers, Centered Dodecagonal numbers, Hexagonal numbers, Triangular numbers.