What is this specific convex polytope called?

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I have the intersection of two spaces:

1) The complete solution to underdetermined matrix equation $Ax=b$ (more rows that columns)

2) The N-Simplex (N is the number of columns/variables in $Ax=b$) defined as: $\sum x_i = 1$ and $x_i \ge 0$

I know the intersection is a convex polytope, but is there a better terminology for it? Perhaps a non-negative convex polytope?