A new lattice model for Monte Carlo simulations of dense polymer melts, developed in the spirit of Verdier-Stockmayer algorithm on square and simple cubic lattices, is presented. By introducing diagonals of squares and cubes as bonds, the lattice model acquires a large number of configurations and wiggling local moves. While it maintains the excluded Volume interactions of monomers, it allows bond crossings and phantom moves, which result in a high mobility of polymers. For an application, we carry out simulations of symmetric A-B block copolymer melts and observe a first-order transition. We also show the stretching of the chains, namely, the non-Gaussian character, as a function of temperature. A quicker evolution towards thermal equilibrium enables us to form an ordered tricontinuous double-diamond (OTDD) phase for linear A-B-C triblock copolymers and a new cylindrical phase for star A-B-C triblock copolymers.