There really IS a polyhedral d1

[jack]

In retrospect, it's obvious. That is the best d1 (one-sided die).

ETA: We went to a little difficulty defining a d1, but it was unspokenly assumed you couldn't build one without cheating a little, eg. ingeniously using a sphere... But this works.

It satisfies all the requirements for a dice. It's solid, uniform, all the faces and edges are straight. It's equally fair rolled on any surface provided with random initial orientations. And if you paint a "1" on the only stable side, it always stops on it!

That's better than we managed for d7! :)

Comments

[pseudomonas.livejournal.com]

Or never stabilises - consider a hamster-ball with an immortal and unsleeping occupant.

[simont]

Hmm. If you change the rules only very slightly, one could argue that a perfect sphere is in fact a d0, on the grounds that it can't be said to have definitely landed in any particular orientation until it's at a stable equilibrium – and a sphere is always in neutral equilibrium, so by that definition it always lands cocked.

[pseudomonas.livejournal.com]

I was assuming that we'd ruled out spheres and was picturing a d100 with internal rodent.

[simont]

AIR we previously considered spheres but assumed that they had one "face" comprising their entire surface, which was always facing upwards when they landed. I'm now revising that definition in the light of clearer thought about what it means for a die to land in a particular way.

[pseudomonas.livejournal.com]

They just feel like the wrong kind of stuff. Similarly, making a cube full of helium that would not land if thrown in air would be cheating.

[cartesiandaemon.livejournal.com]

I was just in the process of suggesting that. Is it cheating more than buttered cats? :) I imagined it perfectly weighted, so it floats up, and bounces off the ceiling, and a few walls, and you *think* it's rolling, and you think it's going to stop, but it stops just sort of floating.

But I want dice that can be any density.

In fact, that could work. Forget helium, throw a solid polyhedron in a closed room with no air and no gravity. It'll roll around, and eventually all the kinetic energy will be absorbed, right? At which point it will be flat to a surface? But if that's not the the floor, you can't read it! :)

[pseudomonas.livejournal.com]

I don't want to play RPGs in a room with no air!

[cartesiandaemon.livejournal.com]

ROFL. That is a perfect sentence :)

[pseudomonas.livejournal.com]

It gave me a chance to use the rodent icon, too.

[cartesiandaemon.livejournal.com]

I thought so. It's sweet :)

[cartesiandaemon.livejournal.com]

I think we *did* argue that :)