15. (15 points) Stack 100 cubes with edge lengths of 1 into a polyhedron, and arrange the possible polyhedra by surface area from smallest to largest, find the first 6.

Stack 100 cubes with edge lengths of 1 into a polyhedron, and arrange the possible polyhedra by surface area from smallest to largest, find the first 6.
【Solution】Solution: From the analysis, we know that when the length is 5, width is 5, and height is 4, the surface area is minimized at this point,  
the surface area is: $(5 \times 5+5 \times 4+5 \times 4) \times 2$
$$
\begin{array}{l}
=65 \times 2 \\
=130
\end{array}
$$

Taking a small cube from the surface of the cuboid with the minimum surface area and placing it on any other part of the cuboid's surface, this adds 4 small squares, making the surface area 134; then taking another small cube and placing it side by side with the first one, this adds 2 more small squares, making the surface area 136; repeating this operation, note that the small cubes taken out are placed side by side with the previous ones, each time adding 2 small squares, so the first 6 in ascending order are: $130<134$ $<136<138<140<142$.