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It's rather a simple question for advanced people.

Consider a 3D Euclidean space: if one is given 2 points, a line can be build that goes through the points; for 3 points -- there is a plane.

For 4D space: a line goes through 2 points and a hyperplane through 4 points.

The question -- what's the name for the object that can be build with given 3 points in 4D space? And more generally, for (N-i) points, 1<i<N-2, in N-dimensional space?

Where can I look for more info on this topic.

Thanks in advance!

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# From plane to hyperplane in high dimension

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