8. (12 points) Fill the ten digits from $0-9$ into the circles in the figure so that the sums of the numbers on the five lines form an arithmetic sequence, and the sum of the terms of this arithmetic sequence is 55. The number of possible values for the common difference of this arithmetic sequence is $\qquad$.

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
【Solution】Solution: According to the analysis, the sum of the arithmetic sequence is exactly 45 more than the sum of the numbers at the five vertices, which is $0+1+2+3+\cdots+9$,

Let the vertices be $A, B, C, D, E$, then $A+B+C+D+E=55-45=10$, among the numbers $0 \sim 9$, only $0+1+2+3+4=10$, so $A, B, C, D, E$ can only be one of the numbers from $0 \sim 4$,

Then the numbers on the other five edges are $45-10=35$,
Let the first term of the arithmetic sequence formed be $a$, and the common difference be $d$, according to the sum formula: $\frac{5 \times(a+a+4d)}{2}=55$ simplifying to: $a+2d=11 \because a \geqslant 0 \quad 11 \geqslant 0+1+5=6$ and 11 is an odd number, $a$ can only take $7, 9$ or 11, $\therefore d=\frac{11-a}{2} \therefore d=2, 1$ or 0,

The corresponding common difference values are: 2, 1 or 0,
Specific filling methods are as follows:
Common difference is 2:
Common difference is 0:
Common
difference
is
1
situation
Therefore, the answer is: 3.