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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

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 7mo 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 7mo 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 7mo 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.

vikingerik 7mo 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 7mo 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 7mo 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.