The shape of a feasible region with equality and inequality constraints

I was wondering if anyone can help me with this (probably basic) question. I want to know how the following feasible region looks like if we have thousands of variables. The constraints are linear. The region is convex and closed. Does the region have a scientific or mathematical name and specific properties (especially for finding projections of vectors on this region)?

\begin{array}{ll} & Ax = b \ & Bx \le d \ &x \ge 0. \end{array}

Thanks a lot for your time and help.