  In this paper, we propose the explicit construction of a new class of
lattices based on polar codes, which are provably good for the additive white
Gaussian noise (AWGN) channel. We follow the multilevel construction of Forney
\textit{et al.} (i.e., Construction D), where the code on each level is a
capacity-achieving polar code for that level. The proposed polar lattices are
efficiently decodable by using multistage decoding. Computable performance
bounds are derived to measure the gap to the generalized capacity at given
error probability. A design example is presented to demonstrate the performance
of polar lattices.
