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​​​​​There is $\textsf{NO}$ base-centered cubic lattice among the list of $14$ Bravais lattices because of one or more of the following reasons

  1. It does $\textsf{NOT}$ have translational symmetry
  2. It is only compatible with the symmetry of orthorhombic crystal system
  3. It is only compatible with the symmetry of tetragonal crystal system
  4. It does $\textsf{NOT}$ have $3$-fold rotation axes along the body diagonals

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