  We obtain a presentation of principal subspaces of basic modules for the
twisted affine Kac-Moody Lie algebras of type $A_{2n-1}^{(2)}$, $D_n^{(2)}$ and
$E_6^{(2)}$. Using this presentation, we construct exact sequences among these
principal subspaces, and use these exact sequences to obtain recursions
satisfied by graded dimensions of the principal subspaces. Solving these
recursions, we obtain the graded dimensions of the principal subspaces.
