The points $A = (-1,1,1),$ $B = (1,-1,1),$ $C = (1,1,-1),$ and $D = (-1,-1,-1)$ form the vertices of a regular tetrahedron.  Find the coordinates of the point $E,$ other than $D,$ such that $ABCE$ is also a regular tetrahedron.
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<|im_start|>user
The points $A = (-1,1,1),$ $B = (1,-1,1),$ $C = (1,1,-1),$ and $D = (-1,-1,-1)$ form the vertices of a regular tetrahedron.  Find the coordinates of the point $E,$ other than $D,$ such that $ABCE$ is also a regular tetrahedron.
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user
\left( \frac{5}{3}, \frac{5}{3}, \frac{5}{3} \right)
The points $A = (-1,1,1),$ $B = (1,-1,1),$ $C = (1,1,-1),$ and $D = (-1,-1,-1)$ form the vertices of a regular tetrahedron.  Find the coordinates of the point $E,$ other than $D,$ such that $ABCE$ is also a regular tetrahedron.
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