Diagonal of parallelogram and parallelepiped

Diagonal — is a line that connects 2 opposite vertices

But for a parallelogram and a parallelepiped definitions of opposite vertices are different.

Opposite vertices of a parallelogram — two vertices that don’t lie on a face.

Opposite vertices of a parallelepiped — two vertices that don’t lie on a side.

And we have a conflict. For example, two vertices that lie on a face of a parallelogram are opposite? If we use first definition then an answer is «Yes!» but if we use second definition then an answer is «No!» IMHO, in the context of a parallelogram the answer should be «Yes!» If we want to determinate if two vertices make a diagonal of a face we should determinate if these vertices are opposite in the context of that face (the face is a parallelepiped). But there is an opinion that we shouldn’t use the definition of opposite vertices: that confuse, must burn in hell, etc.

What opinion is right? I was looking for an answer but I didn’t find.

_Example

$BG$ connects 2 opposite vertices of this parallelepiped?

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