As suggested by Valeriu, you can use Tetrahedron if you give the vertices:

vertices = RandomReal[{0, 1}, {4, 3}];
Graphics3D[Tetrahedron[vertices]]
Graphics3D[Map[InfinitePlane, Subsets[vertices, {3}]], 
 PlotRange -> CoordinateBounds[vertices], 
 PlotRangePadding -> Scaled[.2]]

If you start from the equations of the 4 faces, you can extract the vertices by solving the equations first:

equations = {x == 0, y == 0, z == 0, x + y + z - 1 == 0};
vertices = Map[{x, y, z} /. First@Solve[#] &, Subsets[equations, {3}]];
Graphics3D[Tetrahedron[vertices]]

You may use the same approach, e.g.:

RegionPlot3D[
 x^2 + y^2 + z^2 <= 1 && -x + y + Sin[z]^2 <= 1 && x - y + z <= 1 && 
  x + y - z <= 1 && -x - y + z <= 1 && -x + y - z <= 1 && 
  x - y - z <= 1 && -x^2 - y - z^2 <= 1, {x, -1, 1}, {y, -1, 
  1}, {z, -1, 1}, PlotPoints -> 75, 
 PlotStyle -> Directive[Orange, Opacity[0.777]], Mesh -> None]

Nevertheless, there are some difficulties. If you have 4 surfaces, then the number of possible "polyhedra" is 16. Some of them are not polyhedra but polyhedral sets, i.e.unbounded sets.

Dear Valeriu, I would like to plot a polyhedron trapped between four arbitrary surfaces not only a polyhedron between the coordinate surfaces and other one.