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Comment by gus_massa

9 hours ago

There are only 5 Platonic Solids https://en.wikipedia.org/wiki/Platonic_solid : D4, D6, D8, D12 and D20.

There are 13 more solids with equal faces and vertex (but not equal edges) https://en.wikipedia.org/wiki/Catalan_solid but none of them has 100 faces (It looks like a nice project for 3D printing.)

You can cut the corners, but now the faces are different and ensuring all the faces have the same probability is a nightmare. Some info in https://en.wikipedia.org/wiki/Truncation_(geometry)#Uniform_... (This include the soccer ball.) (I have no idea if this include the D100.)

You also can "cheat" and use https://en.wikipedia.org/wiki/Teetotum that allows any number if you don't care too much about the polyhedral property.

4 comments

gus_massa

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vikingerik  7 hours ago

The Zocchi d100 isn't face-symmetric and thus isn't a fair die. It's as close as he could get. It's really effectively a golf ball with 100 dimples, but they aren't and can't be arranged perfectly symmetrically.

Any even number dX can be made as a fair die as a bipyramid or trapezohedron. https://en.wikipedia.org/wiki/Trapezohedron These would be the only fair face-symmetric d100s. The standard d10 is this, and you sometimes see a d14 or d18 or something like that constructed this way. It becomes impractical with very thin faces past 20 or so. An odd-numbered fair die is also possible by using one twice as big and duplicating the numbers (like 1-5 twice on a d10.)

1313ed01  6 hours ago

Martin Gardner wrote an article on platonic solids in Scientific American, December 1958, and mentioned this in passing: "All five Platonic solids have been used as dice. Next to the cube the octahedron seems to have been the most popular". I have no idea what games using 8-sided dice were somewhat popular (or existed at all) in 1958 or earlier? I wondered about that since I first read that article some decade ago.

I also read a book about games from ca 1880 and it described 12-sided dice (the usual one, numbered 1-12) as if that was a thing some people used for playing games, but none of the games described in that book used them and I also have no idea about other old games using 12-sided dice.

  • bombcar  6 hours ago

    I've seen some octahedrons but they pale in comparison to the six siders - I suspect partially because it's hard to see an octahedron and assume it's fair. It looks like a parallelogram.

    Besides gambling games most dice in antiquity were used in rituals or soothsaying.