How many different 3D parallelepiped are in 4D hyper-parallelepiped?

120 Views Asked by At

Let's say I have three 3D linearly independent vectors, these vectors form a parallelepiped. This parallelepiped has 6 faces, but only 3 of them are "unique" (the other three can be obtained as reflections with $xy$, $yz$ and $xz$).

My question is, what is the rule that defines how many unique faces are in a $n-$dimensional parallelepiped? For instance, a 4D hyper-parallelepiped how many unique 3D parallelepiped would contain?

Thanks!