@Rouben Rostamian  Thank you.
 In the first case, we get to rotate the figure around its axis. This is useful for me, but I wanted to get a little different result.
I guess I did not correctly formulate the question. I wanted that there was an animation of the rotation of the figure around its axis, without the names of its spatial coordinates. How to make axes rotate with the figure?


Plot(P1, axes = normal, view = [-40 .. 40, -40 .. 40, -40 .. -40], orientation = [0, 0, 0], color = blue, thickness = 2)


But about 2 questions.
As can be seen, we take the region of a figure with a thickness of 0, or its cross-section at a given point. With such a display, why does that color fade. Is it possible to change the color of a section in such a record or can you say the selected area?

@Kitonum Thank you!
This really worked.
The questions are already a consequence of using this method.
How to adjust the rotation of this figure around the z axis?
How to make, what color of a figure received in a cut would be much darker?

with(PolyhedralSets);
P1 := PolyhedralSet({-x-20 <= 0, -x-20 <= 20-y, -x-20 <= -(1/2)*y, -x-20 <= -z, -x-20 <= -(x+y)*(1/2), -x-20 <= -(y+z)*(1/2)});
Plot(P1, axes = normal, view = [-40 .. 40, -40 .. 40, -40 .. 40], orientation = [30, -30, -60], color = blue, thickness = 2);
Plot(P1, axes = normal, view = [-40 .. 40, -40 .. 40, -40 .. -40], orientation = [0, 0, 0], color = blue, thickness = 2)