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It is known that silicon fullerenes cannot maintain perfect cage structures like carbon fullerenes. Previous density-functional theory calculations have shown that even with encapsulated species, nearly all endohedral silicon fullerenes exhibit highly puckered cage structures in comparison with their carbon counterparts. In this work, we present theoretical evidences that the tetrahedral fullerene cage Si28 can be fully stabilized by encapsulating a tetrahedral metallic cluster (Al4 or Ga4). To our knowledge, this is the first predicted endohedral silicon fullerene that can retain perfectly the same cage structure (without puckering) as the carbon fullerene counterpart (Td-C28 fullerene). Density-functional theory calculations also suggest that the two endohedral metallosilicon fullerenes Td-M4@Si28 (M=Al,Ga) can be chemically stable because both clusters have a large highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap (~0.9 eV), strong spherical aromaticity (nucleus-independent chemical shift value of −36 and −44), and large binding and embedding energies.