# 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!

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## 2 Answers

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

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If you take two adjacent octants and rotated it, that's the region. For example $x_1\ge 0, x_2\ge 0$, $x_3$ arbitrary. – vadim123 Apr 28 '13 at 23:39

RegionPlot3D[x <= y && y <= z, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}] seems to do the job in Mathematica.

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This picture is deceptive; it suggests that the shape is a three-sided cone. – vadim123 Apr 28 '13 at 20:26
yes, i wish i could have gotten in other coordinate systems too. – Santosh Linkha Apr 28 '13 at 20:28