Clusterfullerenes are capable of entrapping a variety of metal clusters within carbon cage, for which the entrapped metal cluster generally keeps its geometric structure (e.g., bond distance and angle) upon changing the isomeric structure of fullerene cage, and whether the properties of the entrapped metal cluster is geometry-dependent remains unclear. Herein we report an unusual triangular monometallic cluster entrapped in fullerene cage by isolating several novel terbium cyanide clusterfullerenes (TbNC@C) with different cage isomeric structures. Upon varying the isomeric structure of C cage from C(5) to C(6) and to C(9), the entrapped triangular TbNC cluster exhibits significant distortions as evidenced by the changes of Tb-C(N) and C-N bond distances and variation of the Tb-C(N)-N(C) angle by up to 20°, revealing that the geometric structure of the entrapped triangular TbNC cluster is variable. All three TbNC@C molecules are found to be single-ion magnets, and the change of the geometric structure of TbNC cluster directly leads to the alternation of the magnetic relaxation time of the corresponding TbNC@C clusterfullerene.