The eccentricity εu of vertex u in a connected graph G, is the distance between u and a vertex farthermost from u. The aim of the present paper is to introduce new eccentricity based index and eccentricity based polynomial, namely modified augmented eccentric connectivity index and modified augmented eccentric connectivity polynomial respectively. As an application we compute these new indices for octagonal grid

Onm
$\begin{array}{}
\displaystyle
O_n^m
\end{array}$
and we compare the results obtained with the ones obtained by other indices like Ediz eccentric connectivity index, modified eccentric connectivity index and modified eccentric connectivity polynomial ECP(G, x).