You can toy with a normal pen for only a few minutes before you get bored with it. I guessed this to be because it's shape is regular, and your hands quickly become associated with it's shape. Thus, you lose interest and move on to something else in your box of stationary.
Accordingly I came up with a set of design principles.
Must not be too regular
Different parts of it should have different "feels"
Should have moving parts (not always possible, but hey)
Must be small
Must be durable
Must not be able to tear/break something else.
No, it can, and should be symmetrical, but there must be corners, different sorts of corners.
On the one I made I has:
Two cylinders (of differing radius')
A tapered pyramid
The joints between these sections, as well as the edges of the shapes provide irregularities that keep your fingers interested.
When you work with metals, you can get different textures.
If you polish the metal you get a smooth surface
If you grind the metal without polishing at all you get a directional grain
If you use sandpaper you can get a sort of cross-hatch
Those are just the surfaces. For edges:
Edges can be sharpish
Edges can be rounded
Again this increases the irregularity, to keep you amused longer.
Things that move work better too. This is evident by the fact you click pens, spin them, and end up dropping them. By giving the undroppable a moving part, you prevent yourself from dropping it to much. The more movement a part has, the less likely you are to drop it. I used a nut on a threaded section, which you can spin in and out. It is prevented coming off by deforming the thread at the end. A nut is a good choice as it not only rotates, but moves in and out as well. it also has a good selection of edges to toy with.
As you may be able to guess, it is good to be able to carry it with you in a pocket, pencil case or just in your hand. For this reason it is good to keep it to about 5cm x 1.5cm x 1.5cm. Not so small you will drop it, but not so large as to distract others, annoy teachers, or be inconvenient to carry with you.
Assuming you're are at college or school you'll be touching it for a couple of hours a day, and plastics would tend to break after a couple days constant fiddling (look at your pens and count how many aren't missing the bit to latch over a pocket). So, metal or stone it is. I've never worked with stone before, so I decided on metal.
Mustn't tear or break anything else:
Because it would be just great if you put it in your pocket or pencil case, it tore a hole, and vanished. So edges can be somewhat sharp (gives a nice feel to it), but I don't want any edges to be "sharper" than about 60 degrees: an equilateral triangle.
Below is the design I ended up making.