Just had learn the concept of Convex set and Convex Hull.
At this point I had figured of my self regarding the question as following:
"Do I always need to have at least $n+1$ number of elements to construct a convex hull which is embedded in $\Bbb R^n$ space?"
This question is not fully elaborated with a commonly accepted terminologies because of lack of my experience in mathematics so will plot more examples to evade elusiveness.
First, If I have 2-dimensional space, which is correspondent to a sheet of paper , I need at least 3 different elements to construct a polygon which requires at least 2-dimensional space to be fully embedded in it(i.e. triangle would be convex hull which is fully embedded into the 2-dimensional plane with least number of elements).
Also, in a similar vein, If I have 3-dimensional space, which is correspondent to $\Bbb R^3$, I need at least 4 elements or points to construct a 3-dimensional object.
Upon this sense I would like to generalize this idea or notion into n-dimensional sense.
However, where do I have to start from to deal with more or equal to 4-dimensional space which is not visualizable to prove this generalization?
Any related concept or already-existing theorem or statement would be also appreciated.