what are the necessary conditions that are required to prove given vertices to be vertices of various 3-D figures i.e. 3-D square rectangle etc.

Dear Student,
Please find below the solution to the asked query:

Take a group of four vertices and check the coplanarity of the points. If at least one of the group is non-coplanar, then the given vertices are the vertices of a 3-D solid.

If a,b,c and d are any four points, then these are coplanar only ifa-b·a-c×a-d=0

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