I don’t know what to use it for, but I know I want one!
You could just contemplate it.
My God.
It’s full of facets!
Why are non-casino dice so crappy?
A standard casino D6 is larger than a consumer-grade D6, has nice sharp edges, and the numbers are created by embedding an equal-density plastic into the face (as opposed to being painted on or debossed).
Why can’t I get a D8, D10, D12, or D20 that looks like this? This D120, cool as it is, looks no better than the average junk out there. You can get dice in all kinds of sparkly colors but (as best I can tell) nothing with decent-quality construction.
Actually, it’s fairly straightforward. A triacontahedron is just a 30-sided polyhedron: The name just means “30 faces”. “Disdyakis”, in polygon terminology, just means that you stick a pyramid onto each of the faces of the seed polyhedron (I don’t know what the Greek root is for that one). The faces of the triacontahedron (at least, the Catalan one, which is the only one anyone would ever bother talking about) are all rhombi, which are four-sided, and so a disdyakis triacontahedron will have 4*30 = 120 faces.
And Dr. Strangelove, there’s no way you’re going to get “nice sharp edges” on any d120, unless you consider a 165° angle to be “sharp”.
Oh, and I’m also a big fan of all the symmetry they put into the numbers. I’m honestly a bit surprised that that much symmetry is achievable.
I will quibble with one point, though: I’m sort of a Catalan solid fanboy, and the headline is incorrect for me. I’ve known for a long time that I’ve wanted this die.
Yes, 165° can absolutely be made sharp. Casino dice are machined, not injection molded, and on a machined part you could easily notice a 179° edge, let alone 165°.
You can easily see the rounded-off edges and corners in the linked picture. They’re pretty much necessary for an injection molded part since there is a non-zero minimum radius when machining the mold, but I want a part that costs more than 3 cents to manufacture.
For what it’s worth, I have seen a set of machined steel D&D dice. They gave a very satisfying “thud” when they hit the table. I imagine they cost a lot more than standard dice, though.
Steel might be a bit much :). I have a set of these, which are very cool but not particularly fair (especially the D20).
Still, I am tempted to machine my own; perhaps out of aluminum. The workholding is a tad tricky (for everything but a D6, that is), but if you can manage “hold the piece to the cutting bit at this angle”, the rest is trivial.
Have you run the chi-squared test?
Game Science Dice are supposedly made with a high degree of precision, but I don’t know that you need all that precision to mathematically register as a ‘fair die’. Mind you, I don’t entirely understand why the chi-squared test determines randomness, but it kind of looks like it smooths out what looks like ‘hot spots’ on the die and determines evenness in the general distribution of rolled values. Someone want to educate me on this?
A chi-squared test isn’t specific to dice, but a general statistical technique. In general, the question you’re answering with statistics would be something like “Here is the set of rolls I got from this die. How likely is it that I would get this set of rolls, or one basically like it, from a fair die?”. The complication, of course, comes from defining what “one basically like it” means. For instance, if I had a d10 that rolled 3, then 1, then 4, then 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, and 6, in that order, that die would pass most statistical tests (despite not yet rolling a 0: It’s not soon enough to worry about that), but there’s no way in Hell I’d believe the results weren’t being tampered with.
And Game Science talks a good game about how fair their dice are, but given that they’re the makers of the notoriously-biased d100, I’m not sure how seriously I take them.
Dr. Strangelove, I imagine those are 3D printed and then lost-wax cast? I can’t think of any other way to get those shapes, unless you have a mill with an extremely fine and well-articulated head.
Leave it to an Oberlin College professor to do something so great!
There’s actually an even cooler technique out now (well, for a few years). You start with 3D printing, as you guessed–but with steel powder glued together. The object is baked at high temperature and the metal partially fuses together, with the glue vaporized. However, the object is still quite weak and porous, so they then use molten bronze to “infuse” the work. The bronze wicks itself into the object, filling in the voids and making for a strong, solid piece.
Cool, this made the papers. I saw this on Numberphile, where they discussed what actually make a die fair, and had some pretty awesome looking skewed dice. The designer lamented that there wasn’t a way to create a skewed d120, since there’s not enough extra symmetry to distort.
The d120 is just a d60 with its isosceles faces split, to remove the extra bit symmetry. And it is symmetry that makes a die fair.
I have not… I was basing my prediction of unfairness based on the general rolling behavior, and slight asymmetry of the dice. Plus, it seemed like I was getting way too many twenties–maybe just luck, but it looks bad when I say “hey guys, look at these cool dice I just bought” and I start rolling suspiciously well :).
Okay, cool–I hadn’t seen those before. Their D20 looks pretty good–nice sharp edges and painted-on numbers (not as good as molded-in, but better than debossed).
I found this page talking about it, and it does seem to be noticeably better, except for a deviation on 14 caused by some excess flashing. I’d suppose that could be fixed with a bit of sandpaper.
Coincidentally, this story about a dice god appeared a week ago.
A Klien bottle bottle opener made with the process you describe.
http://www.shapeways.com/product/LR5J593S8/klein-bottle-opener
https://www.bathsheba.com/sculpt/process/
Because casino quality dice (a) are more expensive and (b) take much longer to make.
Lou Zocchi used to promote how his GameScience dice were pretty much identical to each other, but apparently they stopped making them in 2013
Ah, OK, I’d heard of sintered metal 3D printing, but I hadn’t heard about the bronze wicking to finish them. This is definitely a cool time to be alive.
Oh, and this is probably a good place to share my 3D designs for the Catalan solids. I haven’t turned them all into dice yet, but I have designed (and printed) a d30.
Last year I noticed someone was selling stainless steel drink cubes (a replacement for ice cubes - they don’t melt in your drink!) at what I thought was an incredibly high price. As I have connections in the steel machining and fabrication industry, I decided to see if I could get them made cheaper and undercut the competition.
I really couldn’t. The cost was very prohibitive, even if you use a cheap grade of stainless, until you got to very large volumes and even then I could not get a cost that made it worthwhile to attempt market entry.
The problem wasn’t the steel. It’s cheap. A set of eight cubes might cost two dollars in material. The problem was getting them made. Machined they were ridiculously out of touch, and even if you had them laser cut from a plate of the right thickness and then polished I still couldn’t get them made for a good price. The retail prices I’d seen were, frankly, what they should have been.
Proper plastic dice will cost MORE than that. Plastic is a bit cheaper than stainless, but that’s not where the cost is. If you want sharp and fair casino dice they must be machined, plus you have the additional step of routing the pips and painting them, which is a few cents here and there and it does add up. Hobbyist/D&D dice could cost an atrocious fortune to go through the same process.
Especially when you consider that polyhedral dice are a much smaller market than d6s, probably even than casino d6s.