Last night I discovered that if you have a need to draw a dodecahedron on paper, label the vertices, and identify the five sets of face diagonals which form cubes, then five is exactly the wrong number of these to search for. Unfortunately, five is unavoidably the number of the damn things there are.

Ah :)

You *might* be able to come up with an algorithm[1] to do it, which would be useful again. Though next time you'd probably have to go through five iterations before being able to use it. But by this argument you come up with a general algorithm for everything, and never do anything.

[1] Dogbert: My algorithm tells us which people to cut from the company to improve efficiency.
Dilbert: I thought you were just firing the people with the highest salaries?
Dogbert: OK, maybe "algorithm" is an overstatement.

Since this is a well-known fact, can you not just find the info online or in a book? Or did you have a masochistic desire to do the hard work yourself? There's even an Escher picture of it, I think, although it wouldn't be called anything useful. But it's pretty :-)

I decided searching for a webpage or book which gave the exact sets of vertices and their interrelation would be slower than drawing a diagram and figuring it out from first principles. There would undoubtedly have been any number of webpages which talked about the concept in general, or showed pretty ray-traced pictures without labelled vertices and without the back side of the solid visible, and sifting through all those for the right one sounded like a longer job than just drawing a diagram and reading vertex letters off it for ten minutes.

heh fair enough

Hmm. When you've found four, isn't the other one rather easy by symmetry considerations? Obviously not, I guess, since if it were you wouldn't have had that experience...