Graph theory has been studied different areas such as mathematics, information and chemistry sciences. It is about descriptors in quantitative structure property relationship (QSPR) and quantitative structure activity relationship (QSAR) studies in the chemical network. Let G = (V(G), E(G)) be a graph without directed and multiple edges and without loops. A lot of topological indices have been defined for QSPR/QSAR studies. There are several types of these indices such as degree-based indices, eccentricity-based indices, and so on. The eccentricity-based topological indices are very important QSPR/QSAR studies, also recently these indices have been studied in many papers. In this paper, some eccentricity-based topological indices namely the connective eccentricity index xce(G), the eccentric connectivity index xc(G),  the modified eccentric connectivity index xc(G),  the total eccentricity index x(G), the Zagreb eccentricity indices M*1(G), M**1(G), M*2(G),   the average eccentricity index avec(G), the eccentricity based geometric-arithmetic index GA4(G) and new version of ABC index such as ABC5(G) have been computed for line and para-line graphs of some convex polytopes Dn, Qn and Rn which are geometric graphs.