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.