minpl(x,y)==plane1(x,y)?2:(minpl(x,y)==plane2(x,y)?3:(minpl(x,y)==plane3(x,y)?4:(minpl(x,y)==plane4(x,y)?5:(minpl(x,y)==plane5(x,y)?6:(minpl(x,y)==plane6(x,y)?7:8)))))

1) In Script window, define functions: Plane1, Plane2, ... for your planes, and minpl(x,y) such as:
    function double plane1(double x, double y) { return    1*x+0*y+0; }
    function double plane2(double x, double y) { return    0*x+1*y+0; }
    function double plane3(double x, double y) { return   0.2*x+0.4*y-1; }
    function double minpl(double x, double y) {return min(plane1(x,y),plane2(x,y),plane3(x,y)); }
2) To make the surface, select "File> New> Function Plot> 3D Function Plot" menu, 
     and enter the formula:
        min(plane1(x,y), plane2(x,y), plane3(x,y)) 
    Set the numbers of Mesh Grids reasonably large not to show the Jaggies.
    We get 3 matrices, and you can delete or hide their plots.
3) Press "D" button at top right corner of the matrix, and select "Add" flyout to add an 
     matrix object, and click "2" image thumbnail in the matrix book to select. 
4) For the color values, select "Matrix> Set Values" menu, and enter the coloring formula 
     using nested conditional operators:
        minpl(x,y)==plane1(x,y)?2:(minpl(x,y)==plane2(x,y)?3:4)
     Here, 2, 3, and 4 are color numbers to be distinguished. 
     (The syntax of the conditional operator is <Condition>?<ValueOnYes):<ValueOnNo> )
5) Make a color-mapped 3D surface plot from the original matrix. Double-click it, and 
    open the Plot Details dialog.
6) Under "Fill" tab, turn ON the "Contour Fill from Matrix" radio button, and select our 
    new matrix object (Mat(2)). 
7) Under "Colormap/Contour" tab, press the Pencil icon for the levels, and enter the 
    From=2(minimum color number), To=4(maximum color number).
8) Customize the color scheme. You can modify a single color at a specific level by pressing its 
    corresponding color swatch. Reducing the number of levels would make the customization easier.
    Click OK to complete the plot customization.
Note that if you want to draw the border lines, show all lines in the Colormap/Contours tab, 
or just use the Draw Line tool.