Solution: With a little commutative algebra, you can prove that 12*volume is an algebraic integer in $\mathbb Q$ adjoin the lengths of the sides. Any continuous function from $\mathbb R$ to a countable set is constant. In fact, the volume is a root of a single polynomial.
Solution: With a little commutative algebra, you can prove that 12*volume is an algebraic integer in $\mathbb Q$ adjoin the lengths of the sides. Any continuous function from $\mathbb R$ to a countable set is constant. In fact, the volume is a root of a single polynomial.