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Polyhedron math problem

  1. Jun 2, 2009 #1
    1. The problem statement, all variables and given/known data

    P is a polyhedron defined by (+/-) x (+/-) z <= 1
    (+/-) x (+/-) y <= 1
    (+/-) y (+/-) z <= 1

    These are 12 inequalities with every possible sign choice taken.

    Is P a regular polyhedron? If so, which type?



    2. Relevant equations

    If we change one inequality to an equation, we get a face of the polyhedron. In order to see if the face is a regular polygon, work out its vertices and/or edge-lengths and/or angles


    3. The attempt at a solution

    I got an octahedron but I see a counterexample of (0.5,0.5,0.5), which seems to satisfy our equations, but not the formula for an octahedron.
     
  2. jcsd
  3. Jun 2, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Polyhedron

    Your 12 inequalities give 12 faces. This is a dodecahedron, not an octahedron.
     
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