Regular Octahedron (AR Modeling Challenge)

The goal of this GeoGebra Augmented Reality modeling challenge is to author 2 surface equations (with domain restrictions) to construct a REGULAR OCTAHEDRON !!! A regular octahedron is one of the 5 main platonic solids. A regular octahedron is made up of 8 faces. Each face is an equilateral triangle. Modeling Clues: Even though there are infinitely many ways to position & size this regular octahedron, for the one in this screencast (below): 1) (0,0,0) serves as its center. 2) Each edge (side of any equilateral triangle) is 6 units long.

Quick Demo