This is a makeover of the "A-Mazing Box" by wizard23 (http://www.thingiverse.com/thing:1481). This version is done in pure geometry on OpenSCAD and requires no images, perl scripts, or bump maps. Maze channels are cylindrical, so the action is very precise and smooth. The box's inner and outer surfaces are smooth. The downside is a very long compilation time in OpenSCAD. The STL files are posted for people who only want to print and have fun with the maze box.
Update Feb. 24, 2015: Created new version that defines the much more difficult inverted box, with the maze printed on the inside of the lid. Pulled the maze definition out into its own include file that can be used for either puzzle. Also uploaded a new, harder maze!
Update December 17, 2015: Noting that the last one I printed is way too tight, I rewrote the openSCAD to expand the lid and outer shell outward by one tolerance. New STL files for maze_box1.stl and maze_box2.stl should fit better.
The OpenSCAD is fully parameterized for all important dimensions such as the box height, radius, size and depth of channels, etc. The maze itself is just a list of line segments, making it very easy for anyone to design their own custom maze. The maze definition is put in its own file, and then a wrapper file is needed to include both the maze definition file and one of the maze box libraries, maze_box_lib.scad or maze_box_inv_lib.scad (depending on whether you wan the maze visible to the solver or not). Use the inclued files "maze_box1.scad" and "maze_box1_inv.scad" as example wrappers. Compile, render, and export from the top-level wrapper file. Note that cylindrical objects like the maze box almost always print better (higher quality) if each cylinder is printed separately, so there is no motion of the extruder path to and from the cylinder exterior. Most slicers should be able to separate the two volumes in the print, so that you can print them separately, if you prefer. Also, if printing with translucent filament, avoid infill or "gap fill" in the walls, but adjust perimeter overlap or extrusion width as necessary to get the cylinders to print walls with three or four perimeters only, which increases the translucence and brings out the color.
The maze definition file in this Thing (and the accompanying STL file) is called "maze1def.scad" and matches the maze in the original A-Mazing Box. To show how easy it is to make a new definition and create an alternative maze box, I have also included a new and harder maze called "maze2def.scad".
I hope that I have made the format straightforward enough that it will spawn many remixes, in which people post their own maze definition files.
I will also give a nod to http://www.thingiverse.com/thing:595481 which I did not know about at the time I wrote the code for this one, but which uses similar OpenSCAD methods to get more or less the same end result, although they have a clever maze definition method using ASCII art.