The extensive search for the global minimum structure of Hf-3 at the B3LYP/LANL2DZ level of theory revealed that D-3h (3)A(2)' (1a(1)'(2)1a(2)''(2)1e'(4)2a(1)'(2)1e ''(2)) and D(3)h (1)A(1)' (1a(1)'(2)2a(1)'(2)1e'(4)1a(2)''(2)3a(1)'(2)) are the lowest triplet and singlet states, respectively, with the triplet state being the lowest one. However, at the CASSCF(10,14)/Stuttgart+2f1g level of theory these two states are degenerate, indicating that at the higher level of theory the singlet state could be in fact the global minimum structure. The triplet D(3)h (3)A(2)' (1a(1)'(2)1a(2)''(2)1e'(4)2a(1)'(2)1e ''(2)) structure is doubly (sigma- and pi-) aromatic and the singlet D(3)h (1)A(1)' (1a(1)'(2)2a(1)'(2)1e'(4)1a(2)''(2)3a(1)'(2)) structure is the first reported triply (sigma-, pi-, and delta-) aromatic system.