# Name of region defined by two points in higher dimensions

Perhaps this isn't the best place to ask, but I'm trying to figure out the proper name for the region that exists in-between two points in higher dimensions. Under certain conditions, n-cube or hypercube would be appropriate, but I'm looking for a more general name.

For example, if the point coordinates are (1,1) and (-1,-1), then the points define a square. The points (-1,1) and (1,-1) define the same region. However, if the point coordinates are (1,1,1) and (-1,-1,-1), then the points define a cube. However, if the points were (1,1,1) and (-1,-1,0), then region defined isn't quite a cube. Same idea applies with more than 3 dimensions.

I ask because I'm trying to name such a space, preferably with 1-2 words instead of a 3+ word phrase.

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"N-dimensional box" or "box" for short. –  Sergei Dec 5 '12 at 0:42

Your are looking for "$n$-dimensional interval" (each coordinate is in a one-dimensional interval).