I'm trying to plot the following implicit equation in 3D:

    Sqrt[x^2+y^2-z^2]+Sqrt[-x^2+y^2+z^2]+Sqrt[x^2-y^2+z^2]=Sqrt[2]

The code I used is:

    ContourPlot3D[Sqrt[x^2 + y^2 - z^2] + Sqrt[x^2 - y^2 + z^2] + Sqrt[-x^2 + y^2 + z^2] == Sqrt[2], {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, Mesh -> None, ContourStyle -> {Red, Opacity[0.5]}, MaxRecursion -> 3]

However, the resulting contour plot is weird:

[![The Plotting result using Mathematica][1]][1]

While the correct result should be something like the following (made with python)

[![The Plotting result using Python][2]][2]

Could someone help me to identify the issue? Thank you!


**Edit:** I know the python result is correct because I tried to calculate a few explicit numerical solutions myself.

I also tried to plot an x-y intersection when z=0.4 to see how it looks in Mathematica:

    k = 0.4;
    ContourPlot[
     Sqrt[x^2 + y^2 - k^2] + Sqrt[x^2 - y^2 + k^2] + 
       Sqrt[-x^2 + y^2 + k^2] == Sqrt[2], {x, 0, 1}, {y, 0, 1}, 
     Mesh -> None, Axes -> False]

[![x-y intersection][3]][3]

The python code I used was (which is from [this answer][4])

    from mpl_toolkits.mplot3d import axes3d
    import matplotlib.pyplot as plt
    import numpy as np
    
    def plot_implicit(fn, bbox=(0,1)):
        ''' create a plot of an implicit function
        fn  ...implicit function (plot where fn==0)
        bbox ..the x,y,and z limits of plotted interval'''
        xmin, xmax, ymin, ymax, zmin, zmax = bbox*3
        fig = plt.figure()
        ax = fig.add_subplot(111, projection='3d')
        A = np.linspace(xmin, xmax, 100) # resolution of the contour
        B = np.linspace(xmin, xmax, 15) # number of slices
        A1,A2 = np.meshgrid(A,A) # grid on which the contour is plotted
    
        for z in B: # plot contours in the XY plane
            X,Y = A1,A2
            Z = fn(X,Y,z)
            cset = ax.contour(X, Y, Z+z, [z], zdir='z')
            # [z] defines the only level to plot for this contour for this value of z
    
        for y in B: # plot contours in the XZ plane
            X,Z = A1,A2
            Y = fn(X,y,Z)
            cset = ax.contour(X, Y+y, Z, [y], zdir='y')
    
        for x in B: # plot contours in the YZ plane
            Y,Z = A1,A2
            X = fn(x,Y,Z)
            cset = ax.contour(X+x, Y, Z, [x], zdir='x')
    
        # must set plot limits because the contour will likely extend
        # way beyond the displayed level.  Otherwise matplotlib extends the plot limits
        # to encompass all values in the contour.
        ax.set_zlim3d(zmin,zmax)
        ax.set_xlim3d(xmin,xmax)
        ax.set_ylim3d(ymin,ymax)
    
        plt.show()
    
    def surface(x,y,z):
        return np.sqrt(-x*x + y*y + z*z) + np.sqrt(x*x - y*y + z*z) + np.sqrt(x*x + y*y - z*z)- np.sqrt(2)
    
    plot_implicit(surface)


  [1]: https://i.sstatic.net/S6kZX.png
  [2]: https://i.sstatic.net/SbBXr.png
  [3]: https://i.sstatic.net/Zvdl6.png
  [4]: https://stackoverflow.com/questions/4680525/plotting-implicit-equations-in-3d