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We have presented topological peripheral shape and distance-based distance measures of 82 fullerene cages C 20  through C 720  on the basis of indices computed from distance matrices such as Szeged index(Sz), Mostar index(Mo), PI-index(PI), Wiener and hyper Wiener(WW) indices. The new results for the Mo, Sz and PI indices of these cages reveal the existence of both isomeric and nonisomeric fullerene cages with the same non-zero Mo indices, and thus we have introduced the novel concept of  isoperipheral fullerene  cages. Moreover we have also found two different fullerene isomers with the same Wiener or hyperwiener or PI indices. Among the fullerene cages that we have studied, C 20 (I h ), C 40 (T d ), C 60 (I h ), and C 240 (I h ) have zero Mostar indices indicating perfect edge peripherality for these cages. A number of isoperipheral pairs of fullerene cages such as  (C 24  (D 6d ), C 28  (T d )), (C 30  (C 2v /1) ,  C 30  (C 2v /2)), (C 32  (D 3h ),C 52 (T)), (C 32  (C 2 ), C 42  (D 3 )), (C 70  (D 5h ), C 78 (D 3h /1)), (C 74  (D 3h ), C 76  (T d )), etc., and the isoperipheral triplet (C 48  (D 6d /1), C 48  (D 6d /2), C 96 (D 6d /1)) are found among fullerenes .

Topological Peripheral Shapes and Distance-Based Characterization of Fullerenes C 20 -C 720 : Existence of Isoperipheral Fullerenes