Crazy coordinates

Geometry Level pending

A polyhedron has the following vertices, for some real number, \(a\):

  • \((e,\pi,a)\)
  • \((\pi,e,a)\)
  • \((-\pi e,8,a)\)
  • \((e^2+\pi,-\pi,a)\)
  • \((-\pi,-\pi^3,a)\)
  • \((\pi, e, a+\pi)\)

And it has a volume of \(20\).

What would be its volume if the last vertex were changed to this?

  • \((6\pi, \pi + 3e, a+8\pi)\)

If you think that it can't be determined, put -1 as your answer.


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