We construct classical solutions of open string field theory which are not
invariant under ordinary twist operation. From detailed analysis of the moduli
space of the solutions, it turns out that our solutions become nontrivial at
boundaries of the moduli space. The cohomology of the modified BRST operator
and the CSFT potential evaluated by the level truncation method strongly
support the fact that our nontrivial solutions correspond to the closed string
vacuum. We show that the nontrivial solutions are equivalent to the twist even
solution which was found by Takahashi and Tanimoto, and twist invariance of
open string field theory remains after the shift of the classical backgrounds.Comment: 19 pages, 2 figures; v2: errors fixe
