1 How many main diagonals does are a 4dim cube Are any two o

1. How many (main) diagonals does are a 4-dim cube? Are any two of them perpendicular to each other? If so, which is perpendicular to which? Are there any diagonals that are not perpendicular to some of the others? if so, what are the angles between them? Justify your answer.

2.For what dimensions n does an n-cube have mutually perpendicular main diagnonals? For such an n, how many diagonals are perpendicular to a given diagonals.