I have not used or seen a solidoodle 4, but as found on the internet, the controller board used in the printer is a version of the Sanguinololu, and the reprap wiki says that
The board is designed to be flexible in its power source, working with
a 12V/5V ATX power supply or any 7V-35V power source via the on-board
if you're using a board not older than V0.7 http://reprap.org/wiki/Sanguinololu
However, I have also found images that show the Solidoodle with this board:
which can be used with 11-15V. This however might be for older versions of the printer.
There are some things to keep in mind: if there is no voltage regulator on the board, make sure that all parts can take the voltage without overheating at some points.