3 ms·

It had never occurred to me that somebody needed to invent polyhedral dice. There must be so many inventions in the world that I’m completely unaware that there

by sd9 6mo ago

It had never occurred to me that somebody needed to invent polyhedral dice. There must be so many inventions in the world that I’m completely unaware that there was a point in time before which something didn’t exist and after that it did, thanks to somebody.

literalAardvark 6mo ago
Everything you've ever seen that isn't sky, water, air, ground, life was invented by someone. Heck, many specimens of the last two are inventions, that are insignificant as a % of species but are in the worldwide top by biomass. It's quite difficult to leave the anthroposphere in much of the world.
gus_massa 6mo ago
There are only 5 Platonic Solids https://en.wikipedia.org/wiki/Platonic_solid 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 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_truncation_in_regular_polyhedra_and_tilings_and_higher 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 https://en.wikipedia.org/wiki/Teetotum that allows any number if you don't care too much about the polyhedral property.
- vikingerik 6mo 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 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 6mo 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 6mo 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.
    - gus_massa 6mo ago
      Slightly related: In a stone shop nearby my home they sell a nice set of Platonic Solids made of semitransparent stones, but the octahedron is an irregular one :((( It's very similar to the ser in this photo https://www.mercadolibre.com.ar/solidos-platonicos-geometria-sagrada-cuarzo-caja-madera/up/MLAU215241895 https://www.mercadolibre.com.ar/solidos-platonicos-geometria... It's a nice present for a friend that is a mathematician too, but there is high chance that they will notice.
amiga386 6mo ago
I too would question the term "inventor" here. * dice: exist for thousands of years * me: what if these had 100 sides? * d100: *invented* A better term would be "creator", because actually creating a 100-sided die that that rolls nicely and each face being equally likely is a lot more difficult than imagining one.

by sd9 6mo ago

literalAardvark 6mo ago

Everything you've ever seen that isn't sky, water, air, ground, life was invented by someone. Heck, many specimens of the last two are inventions, that are insignificant as a % of species but are in the worldwide top by biomass. It's quite difficult to leave the anthroposphere in much of the world.

gus_massa 6mo ago

There are only 5 Platonic Solids https://en.wikipedia.org/wiki/Platonic_solid 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 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_truncation_in_regular_polyhedra_and_tilings_and_higher 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 https://en.wikipedia.org/wiki/Teetotum that allows any number if you don't care too much about the polyhedral property.

vikingerik 6mo 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 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 6mo 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 6mo 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.
  - gus_massa 6mo ago
    Slightly related: In a stone shop nearby my home they sell a nice set of Platonic Solids made of semitransparent stones, but the octahedron is an irregular one :((( It's very similar to the ser in this photo https://www.mercadolibre.com.ar/solidos-platonicos-geometria-sagrada-cuarzo-caja-madera/up/MLAU215241895 https://www.mercadolibre.com.ar/solidos-platonicos-geometria... It's a nice present for a friend that is a mathematician too, but there is high chance that they will notice.

amiga386 6mo ago

I too would question the term "inventor" here. * dice: exist for thousands of years * me: what if these had 100 sides? * d100: *invented* A better term would be "creator", because actually creating a 100-sided die that that rolls nicely and each face being equally likely is a lot more difficult than imagining one.