Robert Dickau has done many nice combinatorial diagrams with Mathematica. For example, here's some i like:
- Bell Numbers @ http://robertdickau.com/bell.html
- All Self-Avoiding Paths Through a Lattice @ http://robertdickau.com/allpaths.html
- Stamp Folding @ http://robertdickau.com/stampfolding.html
You might also enjoy a combinatoric diagram i did. See: Number Of Ways To Loop n Points. (it was done with Mathematica v3. I'll update the notebook to v7 soon.)
Possible loops with 5 points:
Many of Robert's work are about space filling curves. It is one of the math i learned in early 1990s that had a big effect on me. In short, it shows that there are same number of points of one side of a square to the square itself. At the time, it was a shock to mathematicians. See: Space-filling curve, and Xah's Top 10 Math Wonders.