45. Three edges of a triangular pyramid are equal to 1, while the other three are equal to $a$. No face is an equilateral triangle. Within what limits can $a$ vary? What is the volume of this pyramid?
45. $\frac{-1+\sqrt{5}}{2}<a<\frac{1+\sqrt{5}}{2}, a \neq 1$;

$$
V=\frac{1}{12} \sqrt{\left(a^{2}+1\right)\left(3 a^{2}-1-a^{4}\right)}
$$