Volume of a solid bounded by 6 planes I need the volume of a figure delimited by planes
$$ 1 \le x + y + z \le 2 \\
   0 \le x - y - z \le 3 \\
  -1 \le 2x + y - z \le 4 $$
That should hold whenever this sum here :
$$ x \begin{pmatrix}
   1 \\ 1 \\ 2 
   \end{pmatrix} +
   y\begin{pmatrix}
   1 \\-1 \\ 1
   \end{pmatrix} +
   z \begin{pmatrix}
   1 \\-1 \\-1
   \end{pmatrix}$$
belongs to the cube $ (1,2) × (0,3) × (-1,4) $
Thus I suppose I am to scale the cube by the inverse transform to get this volume :
$$ \left| \det \begin{pmatrix}
   1 & 1 & 1 \\
   1 & -1 & -1 \\
   2 & 1 & -1
   \end{pmatrix} ^{-1} \right| * (2-1)(3-0)(4-(-1))$$
Is this correct ?

Apart from a  typo $\bigl((2-0)$ should be replaced by $(3-0)\bigr)$ this is correct.
