Polyhedron Math Problem: Determining Regularity and Type

[wimma]

Homework Statement

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?

Homework 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

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.

 

[HallsofIvy]

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