  Modified teleparallel gravity theory with the torsion scalar have recently
gained a lot of attention as a possible explanation of dark energy. We perform
a thorough reconstruction analysis on the so-called $F(T)$ models, where $F(T)$
is some general function of the torsion term, and derive conditions for the
equivalence between of $F(T)$ models with purely kinetic k-essence. We present
a new class models of $F(T)$-gravity and k-essence. We also proposed some new
models of generalized gases and knot universes as well as some generalizations
of $F(T)$ gravity.
