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Comment by dr_dshiv | Hacker News Reader

I immediately thought of Plato and western esotericism. These look magical. Plato's atomic theory in Timaeus was that atoms should be the simplest geometric forms possible. These are what we now call the Platonic forms: the tetrahedron, the cube, the isocahedron, the octohedron and the dodecahedron. Plato associated each with an element, based on the intrinsic material properties of the geometric shape. For instance, earth was cubic because cubes stack well and fire was tetrahedric because the sharpness of the pyramid-shape was destructive like fire.

Dodecahedra were the 5th element, the quintessence, which was the aether beyond air. Totally magical. These things would have impressed people and communicated philosophical prowess.

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Anyone interested in this kind of stuff (i.e., the Western Esoteric Tradition) would enjoy The Secret History of Western Esotericism podcast. Lots of great scholars and scholarship on this understudied aspect of Western civ. https://shwep.net/

Second. It's the best thing on the internet.

Ok what's the first best thing on the internet?

Thanks so much for this link, I started listening and I immediately love it.

The pentagon and dodecahedron are also very interesting mathematically. Squares and triangles tile the plane, and have nice "round" number angles 90° and 60°. Pentagons don't tile and feature 108° angles. The diagonals of a convex regular pentagon are in the golden ratio to its sides. The inscribed pentagram has a very recursive feel for this reason, "tiling" (nesting) off to infinity.

I'd have to go looking for the paper now but this is fascinatingly true of some kinds of viral envelopes.

Weren’t the Pythagoreans complete number worshippers? Maybe they are related to them?

Yes, like Max Tegmark, they believed the world was made of math. Where harmony means wholeness, they believed in harmonies in numbers (1+2+3+4=10), harmonies in numbers in space (geometry), harmonies in numbers in time (musical ratios) and harmonies in numbers in space and time (astronomy; harmonies of the spheres).

They also conducted the first hypothesis driven experiment in western science when they cast bronze chimes with corresponding ratios of thickness (1:2, 2:3) to see if the pythagorean tuning of strings was a generalizable property.

Plato extended pythagoreanism to make the world of math into the world of pure forms—a universal, immortal realm. He also continued the esoteric tradition of the pythagoreans, who had to keep their practices secret because they kept getting slaughtered.

It's just the best history. Pythagoras was also gender inclusive—not only were there many female pythagorean philosophers, he also (according to aristoxenus) openly credited his moral doctrines to Themistoclea. For integrating science and spirituality at the start of western civ, pythagoreanism is pretty much the coolest.

It’s interesting that such a “scientific” group was readily persecuted. Power fears knowledge it seems.

However very interesting group! Wish they were still around :)

Weird that these are the exact dice used to play a game of Dungeons and Dragons.

Not so weird, you want your dice to be maximally symmetric for fairness. When you add easy manufacture to the qualifications, only the platonic solids will do.

The d10 is not a platonic solid.

That is correct, I'm an idiot. Almost only the platonic solids will do? Honestly it seems like the platonic solids are the easiest to work with, except percentile dice are nice for people using base-10 so you have to throw in a 10-sided die too. There are non-platonic versions of the other dice too, but you don't see them I assume because they're harder to manufacture. Less cut and dry than I though though!

The original D&D dice were the 5 platonic solids, the 10s were added later. But there are lots of shapes that can be "fair". You can stick 2 pyramids with any number of sides together, you can make a long prism with any number of sides since it will never land on the long ends, a coin can be considered to be a 2 sided die. I seem to recall somebody made a 30 sided die where the sides were parallelograms, although I never had one.

> The original D&D dice were the 5 platonic solids, the 10s were added later.

True; IIRC, the rules used d10 but it was a way of reading the d20 before d10s were manufactured.

yup the original d20's were labeled 1-10 twice, and you used a crayon to colour the on set differently. If it landed on your "blue" 10 it was a 20, if it landed on the uncoloured 10 it was 10 for example.

Any regular bi-pyramid would be technically fair. I think it's just that you tend to get rounder dice by using platonic solids or tesselating / modifying platonic solids.

By the way, you can get d100 dice.

> By the way, you can get d100 dice.

Can you get fair d100s, though?

I know the “Zocchihedron”, one of the first and best known commercial ones, is not fair (after this was proven, they were renumbered so that the over-/under-weighted results were better distributed over the range, but it's still not fair.)

Wow, I'd seen one but never actually checked whether it was fair.

Yes. By trivial example, two fifty sided pyramids joined at the base. These can be purchased.

Most players use d10 pairs with a tens die, though, because they roll better.

Also a 100-sided cylinder. Probably hard to read though.

Do you have a link for the pyramid one?

No. I bought it 25 years ago in a game store called "Games Unlimited" in Pittsburgh, PA.

> Most players use d10 pairs with a tens die, though, because they roll better.

There's also a nifty trick used in many RPGs based on d100 to roll once and have 2 d100 numbers (by inverting the result).

So for example in Warhammer you roll d100 for attack, you hit if your result is lower than your Melee Combat attribute, and the inverted result shows which part of the enemy body you hit (that influences critical hits and armor).

All that is required for fairness is equal faces and equivalent reach behavior.

Every total symmetry fits. You don't need a platonic solid. By example, every even number six or up can be fairly represented as two pyramids joined at the base.

Many fair non-platonic dice exist besides the d10, such as the d30. Go ask at the game store

I actually own a d30, as well as a super weird looking d3. But you don't generally see non-platonic solids for anything but a d10. Why? My guess was ease of manufacture, but honestly IDK.

There are only 5 platonic solids, and dungeons and dragons dice use all of those. So it's not weird.

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