Can anyone tell me what is the plot for max(abs(x),abs(y),abs(z))=1

Question

max(|x|,|y|,|z|)=1

Can anyone please tell me how to plot this equation? Thanks

Answer 1

The points such that $\max(|x|,|y|,|z|)\leq1$ are does in which $x,y$ and $z$ are all in $[-1,1]$. In other words they form a cube.

The points such that $\max(|x|,|y|,|z|)=1$ are those in which at least one of the points is equal to $\pm1$. These are the faces of the cube.

Answer 2

The surface of the cube with vertexes in $\lbrace |x|=1,|y|=1,|z|=1\rbrace$