With dilation 2, congestion 2, expansion 3/2, and load 1, this short paper first presents a parallel method for embedding a pyramid with height n, Pn for n ?2, into a (2n - 1) - dimensional hypercube, H2n - 1, in O(n) time. With dilation 2, congestion 2n - t + 3 (or 2n-t+1 + 2), and load when 0 ?k = 2t (or k = 2t - 1) ? 2n - 2, our proposed parallel method is further extended to map Pn into Hk with load balancing in O(k) time.