name for a vector-operator which returns the set of the combinated coordinates

Question

I am searching for a vector operator which combines two vectors and returns the possible combinations of these vectors.

For example: $(1,2) ? (3,4) = \{(1,2),(3,2),(1,4),(3,4)\}$

I need this because I want to produce the set of corners of an axis aligned cuboid given the minimum and the maximum corner.

It would be great to get some tips what to search for, a solution or some links to a problem like the one with the cuboid.

Edit: I just got the tip, that it similar to the database join operator. Is there a mathematical equivalent for this?

Answer 1

I just noticed that there is a difference between the cross-product and the cartesian product but they are using the same operator sign.

https://en.wikipedia.org/wiki/Cartesian_product

I should have known this, because it is used to define cartesian coordinates. For example $N^3= \mathbb{N} \times \mathbb{N} \times \mathbb{N}$, which is doing exactly the same thing.