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Dice Survivor, Round IV

Which die won't be part of the trio in round 5?

  • d6. They're not fancy enough.

    Votes: 48 34.8%
  • d8. They're in the game just because Gygax & Arneson were lazy.

    Votes: 30 21.7%
  • d10. They're unclean. Just unclean.

    Votes: 50 36.2%
  • d20. They aren't a damage die anymore since the monks were revised.

    Votes: 10 7.2%

Gez

First Post
After eliminating the d3, d4, and d12, now is time for Round 4! Ready to Rumble!

And the Math Teacher Award goes to Orsal, who demonstrated to us why the d10 is unclean and need to be voted off ASAP:
orsal said:
A bit more: there are three kinds of symmetry a polyhedron can have (well, there are more, but three that I'm discussing here): Vertex-transitivity, meaning that the geometry of the solid itself can't distinguish any vertex from any other; Edge-transitivity, meaning that pure geometry can't distinguish any edge from any other; Face-transitivity (you get the pattern). By "pure geometry", I mean the shape of the die, ignoring labels. You can tell the difference between the face of your d6 labelled "6" and the face labelled "2" because, well, one is labelled "6" and the other is labelled "2". But if you were able to obliterate the labels, the die would look exactly the same with the "6" on top as with the "2" on top.

The five platonic solids are the only polyhedra which are both face-transitive and vertex-transitive. It's not hard to show, with a little high-school level mathematics, that there are only those five, and you end up getting edge-transitivity for free. But if you demand only one kind of transitivity, there are infinitely many possibilities. All your more exotic dice (by "more exotic" I mean "not included way back when", so the d10 counts) are face-transitive but not vertex-transitive or edge-transitive. If you think a little about it, face-transitivity is what you want in a die. It guarantees that all faces are equally likely. Vertex-transitivity doesn't really matter, and I don't understand the purists who think the lack of vertex-transitivity is a point against the d10.

That said, death to the d6. They're boring.
 

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