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The six points listed in the question are in the same plane.

One can check that by doing a list_plot, or a point3d, or by constructing the polyhedron with vertices the points in the list.

Here are the corresponding commands.

$ sage
SageMath version 8.2.rc1, Release Date: 2018-03-31
sage: p = [(-1, 2, 3), (2, -1, 3), (3, -1, 2), (-1 ,3 ,2), (2, 3, -1), (3, 2, -1)]
sage: list_plot(p)
Launched jmol viewer for Graphics3d Object
sage: point3d(p)
Launched jmol viewer for Graphics3d Object
sage: po = Polyhedron(p)
sage: po
A 2-dimensional polyhedron in ZZ^3 defined as the convex hull of 6 vertices
sage: po.show()
Launched jmol viewer for Graphics3d Object