They specifically didn't say it was a hypercube, so I'm going to assume its a normal cube traveling through time and say that it could get to a max of 5 faces by moving forward 3 times, turning 90 degrees and moving forward again. The 6th face can be reached, if the cube's gravity-well is high enough, by getting a really good running start and jumping over the next to land on the 6th, Otherwise the ant is fucked and his father is very disappointed in him.