What does $\{(x_1, x_2, x_3) \in\mathbb R^3: x_3 \leq x_2 \leq x_1 \}$ look like? What does $\{(x_1, x_2, x_3) \in\mathbb R^3: x_3 \leq x_2 \leq x_1 \}$ look like? 
It seems to be a linear convex cone with vertex at the origin.
I am trying to visualize it but cannot. Thanks!

$x_2\ge x_3$ is a closed halfspace.  $x_1\ge x_2$ is also a closed halfspace.  Your region is the intersection of these two halfspaces.
