# Is there a term to conv$\{x_1,...,x_n\}\subseteq\mathbb R^n$?

Suppose I have $$n$$ vectors in $$\mathbb R^n, \{x_1,\ldots,x_n\}$$ s.t. any $$x_k, 1\leq k\leq n$$ "opens" a new dimension. (For example, no $$4$$ vectors of $$(x_i)$$ lie on a same plane, and bo 3 vectors lie on the same line, etc).

Is there a name in such a case to $$\text{conv}\{x_1\ldots,x_n\}$$ for some general $$n$$?

For example, if $$n=1$$ then this is a dot. If $$n=2$$ this is a segment. If $$n=3$$ this is a triangle.