With last generation 3D printers you can now easily create a very detailed product. In this trend, every 3D software acquires an enhanced importance. You can indeed turn your own design in reality, and whether it is a toy, a tool, or a prototype scale-model, you will see that it will come out an awesome piece of art.
A puzzle game composed by a dozen of 3D tiles can be printed to reach a remarkable size, and it will be a very appreciated present. If Easter is coming you can also decide to make an egg shape instead of the classical cube.

Step 1: The Basic Shapes

One of the professional software used to model architectural and mechanical shapes is Rhinoceros (Rhino for friends). This software lets you to model 3d geometric objects keeping the vector format through all the designing process, with a great improvement in precision and detail.
Draw a cube with the right dimensions, or an egg applying the revolve command to a simple curve. Since I'm not skilled enough to teach advanced modeling in Rhino, I will use basic commands which are easily found in main toolbar or menu list of the software.

Step 2: The Power of Parameters

Grasshopper is a very powerful plugin for Rhino. With its features you can apply algorithmic formulas to the geometric shapes of Rhino, and a fast parameters variation will update instantly the 3D model. It also can generate very complicate parametric geometry which is otherwise very difficult, if not impossible, to draw with standard modifiers.
You can analyze the schematic to see which commands are used and how they are connected. I added a few notes over the images, so that you can find out the full name of each function.

Step 3: The Subdivisions

As you can recognize, I used the Voronoi3D feature to subdivide the volume of the cube or the egg in a number of different solids, each boundary with the near ones. Then I used the points from FaceNormals command as centre for each little sphere which acts as joints between the 3D tiles. These spheres protrude from a tile and are subtracted from the adjacent ones.
Probably there is a faster way to subtract spheres from solids and to join them to other tiles in Grasshopper, but I couldn't find it, so I had to do that in Rhino. So, after baking both Voronoi solid and spheres group, turn off the Grasshopper plugin and go working on Rhino window.

Step 4: The Choise

With the SelDup command select the duplicated spheres and delete them.
Now you can proceed in different ways. I decided to hide one tile at a time, the I deleted the unwanted spheres and hid the spheres I decided to keep. Go on in this way until nothing is shown. Then unhide everything.

Step 5: Fusion

Now you can Boolean union the external spheres to the tiles. Anyway if you don't like that style you can choose to delete them too, and keep flat faces on the cube. I wanted to add more difficulty in solving the puzzle.

Step 6: Subtract

Then select all the (remained) spheres and subtract them (Boolean Difference) from all the cube together, but keep the input solids.

Step 7: The Joints

This is the difficult part. You have to choose which side the spheres would stay. You can also use Ghosted view to see better inside the cube. When you have decide select the sphere and the corresponding tile, then join them with Boolean Union. If all the spheres around a tile have been examined, hide that tile and carry on.
Try to not protrude spheres all around the same tile, because it would simplify the game too much.

Step 8: The Egg

I will save you from hearing a joke about Columbus' Egg...
I found some problem in setting the points inside the egg, anyway I made a Boolean Intersection between each tile and the egg. Now I have to choose the spheres in the same way I used for the cube.

Step 9: Blending

If you wish, you can smooth edges with the Blend Edge command. Better you make it before subtracting the spheres, so to select all the edges in one time.

Step 10: Time to Play

Now you only have to save the pieces in one or more .stl file (it's in the export options of Rhino) and send it to the 3D printer.
There is a "nota bene" to add: there are some chances that the puzzle will not work.
This could be due to two causes: first the rigidity of the printed piece and material, among with the percentage of filling chosen in printing settings. Second the reciprocal disposal of the tiles' faces. Indeed, since some tiles will certainly be blocked by the others, I'm not sure that every tile will be able to be inserted.
Of course the bigger is the number of tiles, the harder will be inserting them... you only have to try.

Step 11: Enjoy With Colours

You can of course paint the pieces or print them with different colours.
I hope you will be able to model your own puzzle, since I still have to set up the STL files, but I will attach them in next weeks.
Enjoy!