# What is this specific convex polytope called?

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?

• "All equalities and positivity" looks like one of the standard forms in the Simplex method. Since any polyhedral set (a convex polytope, in particular) can be reduced to this form I will be surprised if it has a special name. – A.Γ. Aug 14 '15 at 0:30
• @A.G. Alright. Thanks a lot for letting me know! – Andy Yao Aug 14 '15 at 0:49