2. (20 points) Place 9 different natural numbers on the 8 vertices and the center $O$ of a regular octagon, such that the sum of the 5 numbers on each pair of parallel sides and the center $O$ equals the sum of the 8 numbers on the vertices. The smallest number at the center $O$ is . $\qquad$
【Analysis】Let the 9 numbers be $A, B, C, D, E, F, G, H, O$. Then, according to the problem, set up the equations and find the minimum value of $O$.

【Solution】Solution: According to the problem, we have: $A+B+E+F+O=B+C+F+G+O=C+D+G+H+O=D+E+H+A+O=$ $A+B+C+D+E+F+G+H$,

Simplifying, we get: $A+E=C+G, B+F=D+H$,
So $A+B+C+D+E+F+G+H=2 O$,
That is, when $A, B, C, D, E, F, G, H$ are $0,1,2,3,4,5,6,7$, $O$ is minimized, i.e., $O=\frac{1}{2} \cdot(0+1+2+3+4+5+6+7)=14$.

Therefore, the answer is: 14.