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var ('x, y, z') implicit_plot3d (abs (x) + abs (y) + abs (z) - 1, (x, -1,1), (y, -1,1), (z, -1,1), color = 'aquamarine ')

var ('x, y, z') z') # with SageMath 7.3

implicit_plot3d (abs (x) + abs (y) + abs (z) - 1, (x, -1,1), (y, -1,1), (z, -1,1), color = 'aquamarine ')

var ('x, y, z') # with SageMath 7.3We know that $|x| + |y| - 1 = 0$ is the equation of a square having its vertices on the axes.

implicit_plot3d (abs (x) I asked to represent the equation $|x| + abs (y) |y| + abs (z) |z| - 1, 1 - 0$, believing to obtain a cube in space.

But I obtain an octahedron. Why? And how do you get a cube?

# with SageMath 7.3
var('x, y, z')
f = abs(x) + abs(y) + abs(z) - 1
implicit_plot3d(f, (x, -1,1), -1, 1), (y, -1,1), -1, 1), (z, -1,1), color = 'aquamarine ')
-1, 1), color='aquamarine ')

We know that $|x| + |y| - 1 = 0$ is the equation of a square having its vertices on the axes.

I asked to represent the equation $|x| + |y| + |z| - 1 - 0$, believing to obtain a cube in space.

But I obtain an octahedron. Why? And how do you get a cube?

# with SageMath 7.3
var('x, y, z')
f = abs(x) + abs(y) + abs(z) - 1
implicit_plot3d(f, (x, -1, 1), (y, -1, 1), (z, -1, 1), color='aquamarine ')