implicit function for rectangle cuboid

Question

I know the implicit function for a cube is max($\lvert x \lvert, \lvert y \lvert, \lvert z \lvert) = 1$. What's the implicit function for a rectangle cuboid with any given height, width and length?

Thank you in advance!

Answer 1

Just normalize the variables and shift to get a cuboid anywhere, any size:

$$ \max\left\{ \frac{|x|}{a} + d, \frac{|y|}{b} + e, \frac{|z|}{c} + f \right\} = 1 .$$