# Wire Frame Cube Moment

A cubic wire frame consists of 12 segments interconnecting 8 vertices. The vertices are located at the following points:

\begin{align} (x,y,z) = &(-1,1,1),(-1,-1,1),(1,-1,1),(1,1,1),\\&(-1,1,-1),(-1,-1,-1),(1,-1,-1),(1,1,-1). \end{align}

The wire frame has a mass $$M$$ which is uniformly distributed over its constituent line segments. The object's moment of inertia with respect to an axis perpendicular to the $$xy$$-plane and passing through the point $$(x,y) = (0,0)$$ can be expressed as $$\dfrac{a}{b} M$$, where $$a$$ and $$b$$ are coprime positive integers.

Determine $$a + b$$.

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