15. (20 points) A cube with six faces labeled $1,2,3,4,5$, and 6 is called a die. Answer the following:
（1）How many different dice are there;
(2) The absolute difference between the numbers on two adjacent faces of a die is called the variation between these two faces, and the sum of all variations is called the total variation $V$. Among all dice, find the maximum and minimum values of $V$.
15. (1) Suppose there is a square on the table that is congruent to the side of a die. Placing a die on this square can be done in $6 \times 4$ ways. Therefore, the number of different dice is $\frac{6!}{6 \times 4}=30$.
(2) The variations produced by the six numbers from $1 \sim 6$ are 15 in total, and their sum is
$$
\begin{array}{l}
1+(1+2)+(1+2+3)+(1+2+3+4)+ \\
(1+2+3+4+5)=35 .
\end{array}
$$

Compared to this, in the total variation of each die, what is missing is the variation between the numbers on the three pairs of opposite faces, denoted as $v$, then
$$
\begin{array}{l}
v_{\text {max }}=(6+5+4)-(1+2+3)=9, \\
v_{\text {min }}=1+1+1=3 .
\end{array}
$$

Therefore, $V_{\text {max }}=35-v_{\text {min }}=32, V_{\text {min }}=35-v_{\text {max }}=26$. (Provided by Kong Xiangxin)