# A weird tetrahedron? No?

Geometry Level 3

Let $$V$$ be the volume of a tetrahedron bounded by the coordinate planes and the plane $$\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$$ where $$a$$,$$b$$,$$c$$ are positive real numbers.

If $$V$$ can be written in the form of
$\large \frac{2^{\zeta}a^{\alpha}b^{\beta}c^{\gamma} } {144^{\xi}}$

where $$\zeta, \alpha, \gamma$$ and $$\xi$$ are positive integers, what is the value of $$50\lfloor \zeta + \alpha + \beta + \gamma + \xi \rfloor$$?

###### Image Credit: Wikimedia Symmetries of the tetrahedron.
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