In accordance with the geometrical relationship between an icosahedron, a tetrahedron and a carbon cage cluser, a method is devised to assemble giant fullerenenes (between C100 and C400) of icosahedral and tetrahedral symmetries by using a triangular motif. The optimized structures and diameters of these giant fullerenes are generated. Their electronic structures are also determined by applying the EHT method. The closed-shell configurations of the giant fullerenes are deduced. The hyperfullerenes, C60, C240, and C540 with Ih symmetry, as well as C56, C188 and C392 with Td symmetry, are predicted on the basis of their electronic structures and cage diameters.