Plotting linear inequalities in Mathematica

Question

I have linear systems of inequalities in 3 variables and I\'d like to plot these regions. Ideally, I\'d like something that looks like objects in PolyhedronData. I tried Reg

Answer 1

Seeing all the previous answers; what is wrong with using the build-in function RegionPlot3D, e.g.

RegionPlot3D[  2*y+3*z <= 5 &&  x+y+2*z <= 4 && x+2*y+3*z <= 7 &&
               x >= 0 && y >= 0 && z >= 0,
             {x, 0, 4}, {y, 0, 5/2}, {z, 0, 5/3} ]