Visualizing 3D polyhedra

Credit

This tool is jsut an interface to [Sage](https://www.sagemath.org/). SageMath is a free open-source mathematics software system licensed under the GPL. [SageMathCell](https://sagecell.sagemath.org/) project is an easy-to-use web interface to a free open-source mathematics software system SageMath. It allows embedding Sage computations into any webpage. Resources for your computation are provided by SageMath, Inc..

This tool calls the `Polyhedron` class to define your polyhedron. The argument `ieqs` is a vector of vectors \( [d, a, b, c] \) to indicate constraint \( ax_1 + bx_2 + cx_3 + d \ge 0 \). Then, `plot` is called on that object. For instance, the following Sage command will plot \( X \) defined below.

Polyhedron(ieqs = [[2,-1,-1,-1],[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,-1,0,0],[1,0,-1,0],[1,0,0,-1]]).plot()

$$ X = \left\{ x\in\mathbb R^3 : \begin{array}{ll} x_1 + x_2 + x_3 \le 2 \\ x_1 \le 1 \\ x_2 \le 1 \\ x_3 \le 1 \\ x_1 \ge 0 \\ x_2 \ge 0 \\ x_4 \ge 0 \end{array} \right\} $$