Ignore the paper size, I meant to make it larger before posting. :-(
This is the best comic I've read so far!
I believe the original problem statement is stated wrongly here. Even on a plane, one only needs to draw three horizontal lines to connect all 9 dots. To pose the usual challenge, the question must state "... four connected straight lines".
"... four connected straight lines" doesn't work either, because then you could just draw three horizontal lines and one vertical to connect them all.
http://i7.minus.com/ibs8O81MUcHWX4.png shows how to do this with 3 lines.
I'd like to see that second fold pulled off...
Assuming the dots are 1 inch apart, give me a 5 inch paintbrush and I'll do it in one line.