Similarly, the EoS parameter ω becomes 6 We would also comment that the case of vanishing pressure p = 0 (dust) is not allowed in the present formalism since it will make f ( r ) unbounded. The dust cases in the framework of braneworld wormholes are investigated in [22, 23]. The specific dimensionless parameter ξ , defined by ξ = ( p − ρ ) / | ρ | , characterizes how the exotic or normal matters are distributed around the wormhole’s throat [4, 15]. The exoticity at or near the throat of the wormhole is required to be non-negative, ξ > 0. The positivity of the exoticity ensures that wormhole will satisfy the flare-out condition as well. From Eq. (15), the exoticity becomes In Fig. 5, we have plotted the exoticity against the radial coordinate. It shows that the exoticity remains positive while it converges to zero for large r . Hence the wormhole is surrounded by the exotic phantom energy, right from its throat to a sufficiently large distance. This also suggests that we can construct a wormhole with a sufficiently large radius that could be traversable for two dimensional beings. In summary, our objective in this article has been to present a mathematical prescription for obtaining a wormhole in low dimensional spacetime. The wormhole is supported by an external source of phantom energy which is anistropically distributed. The wormhole spacetime satisfies a variable equation of state, which is in good agreement with earlier models available in the literature. It is also shown that the otherwise asymptotically non- flat wormhole could be converted to an asymptotically flat one by matching the various components of its metric with the exterior BTZ spacetime. [1] M. Visser, Lorentzian Wormholes: From Einstein to Hawking, (Springer-Verlag New York, Inc, 1996) [2] M. Jamil et al, arXiv:0906.2142v1 [gr-qc] ω ( r ) = $^{√}$1 − r 1+ m b$_{0}$ (5 + m ) ( m + 1)$_{2}$ F$_{1}$ ( 5+ m 2+2 $_{m}$, 1 $_{2}$, 7+3 m 2+2 $_{m}$, r 1+ m b$_{0}$ $_{)}$. (24) | ρ | ξ = − b$_{0}$ ( m + 1) 16 πr m +3   $^{√}$1 − r 1+ m b$_{0}$ (3 + m + 2 α ) ( m + 1)$_{2}$ F$_{1}$ ( 3+ m +2 α 2+2 m , 1 $_{2}$, 5+3 m +2 α 2+2 m , r 1+ m b$_{0}$ ) − 1$^{}$ $_{}$. (25)