Context:
I will be teaching 11-16 year olds about prisms.
After reading this article, it remains unclear to me what exactly a right prism is:
A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies iff all the joining faces are rectangular.
It seems to me that whether a prism is right or not depends on a choice of base for the prism.
I would like to be able to show them real prism-like figures, or pictures of prisms and ask them to describe them as right or oblique. It could very well be that the answer does and should depend on orientation, but this is not clear to me.
Example:
Take for instance a prism four of whose faces are rectangles and whose remaining two faces are non-rectangular parallelograms. If we choose the base to be one of the non-rectangular faces, then this seemingly is a right prism. If we choose the base to be one of the rectangular faces, then this seemingly is not a right prism, but rather an oblique prism.
If "rightness" depends on a choice of base
One way to remedy the highlighted description would be to say that a prism always comes with a choice of base.
If "rightness" does not depend on a choice of base
Another way would be to say that a prism is right if there exists a choice of base such that it satisfies the conditions in the highlighted description. A more pragmatic way would be to say that a prism is right if it has at least four rectangular faces.
Question
In what sense is it well defined to call a prism "right", and is there a consensus on the terminology?
The bases must be congruent and parallel and oriented in such a way that you can translate one onto the other.
A prism is a right prism if all of the lines connecting corresponding points of the bases are perpendicular to both bases.
Right and erect are both derived from the same root word.