Yeah, and still easy to buy and fairly cheap too, never really got the obsession with the digital ones that drift and can't measure accurately if they happen to go flat when the proper vernier ones just work
If I am not mistaken, you can take the Minkowski sum of two bodies of constant width and get another such body. So for smoothing you could just add a ball.
Awesome! I've designed and made (with resin moulding) some D4 dice that tumble more satisfyingly than standard D4 dice, but with all flat faces. That took a little bit of working out to get the way I wanted them, because there are a lot of options for how to go about it, but it is so satisfying to have them in hand. Needless to say, this video is delightful.
@@henryseg A few. Namely a tetrahedron base and also a prism base, but with cuts that create new faces which the die can't land on (on a level surface). I created more than one version of each, since there are different ways of doing it. I wouldn't know how to describe the ones that I ended up with specifically.
I feel like the lack of sharp corners provides the opportunity to do away with the slightly confusing multiple numbers per side aspect of traditional D4s. Surely the curve on the corner is smooth enough that you could just put one copy of each number right on the tip, right? I think that would be cool.
@@Canyon_Lark I think we were concerned that the numerals there, at the points with the most curvature, might be bad for rolling a book on top of them.
well I mean in a pure mathematical sense, of course there's a difference, but if you were to construct it, there would be no functional difference I mean
i like that these are not only very cool dice, but also a great geometry deep-dive, due to manufacturing limitations regarding the reuleaux spheroform. i got a truncated tetrahedron in my last dice lab order, so even though this would still roll much better, i can't justify a functionally similar purchase at the moment! very cool though!
Pretty weird to say that the sphere doesn't have the tetrahedral symmetry. It certainly does, and more. Of course its problem is that it won't stop rolling, which I would rather phrase perhaps as "doesn't have _only_ the tetrahedral symmetry". At the Museum of Math in NYC you can ride in a rowboat over a small lake of these, and due to the constant width it's not a bumpy ride.
Great question! It isn’t clear if it will work with the other solids. You have to do some sort of average of shapes over the different symmetry transformations, and the worry is that it averages out to give you a sphere.
The tetrahedron has faces opposite vertices, while all the other Platonic solids have faces opposite faces, vertices opposite vertices. I reckon that rather spoils things.
@@henryseg I don't see how those can be made of constant width. The whole Reuleaux construction that leads to the Meissner tetrahedron relies on vertices being opposite the faces. If a polyhedron has opposite parallel faces, it seem to me the only way to make it of constant width is if both become spherical centred around the polyhedron centre, which defeats the purpose of a die. There might be something possible with odd bipyramids or even trapezohedra, but I'm not at all sure about that.
I've been looking into the constant width shapes of four sides for the last couple of months. It seems odd to me because they were talked about on TH-cam about five years ago. Is there a more flexible way to model these with mathematical formulas other than with OpenSCAD?
Your orbiform seems to have a center. Slice the orbiform with a plane through the center. You get a 2-dimensional shape of constant width. Could such a shape have n "sides" and "rotational symmetries" for n>3?
I've had a concept for a special d30 design that I've always wanted to see in action, and I even have a prototype modeled in Blender, but I lack the resources to actually manufacture or distribute it. Can I get in touch via business email, and discuss it under NDA?
@@BallstinkBaron I used a d30 heavily as an aid to thinking while working on a particular projection from 6D to 3D. Outside of that there are sadly few games that use it... but it's a super pleasant shape (the rhombic d30 anyway -- imveryangry must have thought of a different way to do it). @imveryangryitsnotbutter, I'm just guessing here but you may have trouble getting a mathematician under NDA. Not only is communicating insights their whole livelihood, but they're also part of a discipline that's already thought of lots of theoretical ways of making dice. You may want to have the NDA give them an "out" if your invention has already been written about.
@@dranorter Maybe an NDA is excessive. What I really mean is some kind of legal contract which says: "Do not sell this design on your store or share it with people who might try to sell it, unless you first pay me an amount of money up-front as compensation for my work (negotiable)." And I guess a clause stating "If you can prove that this design already existed before I proposed it, this contract is null and void."
Man, Euler invented everything. Even when you think there's something new like "solids of constant width," nope, Euler ran down to the trademark office before you.
Does the weight of the paint effect the outcome? Visually, 3 and 4 look to have more surface area (more paint, more weight) than 1. Maybe this is a solved problem though and the manufacturing process uses a consistent amount of paint for each number?
If you want that level of precision in your dice, you’re looking at casino dice, which are milled rather than injection molded, and the pips filled in with material of the same density as the rest of the die. The impression I get is that there are far larger sources of error than amount of paint on different parts of an injection molded die!
i found it interesting when you rolled a book on them. i have so many questions like for instance: can you rotate the book without losing grip of each dice to the floor and the book? how many degrees of freedom does rolling a book have on differently shaped dice? how many dice can you add under the book before rolling it becomes impossible? (without losing grip?)
at a molecular level: I wonder if, if we were to roll it an infinity amount of time, if there wouldn't be a biased number due to the material not being 100% perfect all around, ain't no way all the molecules are arranged perfectly all the way. I'm sure on a small scale it's unnoticeable, but on a larger scale are dices a real way to obtain random numbers. Or could we expect a number to happen more frequently. It would made sense to me.
Wait... Are you.. what, ah. I didn't know you were so close! Aaaahhh! A local dice company! Now I have to share this with the local game shops I visit. So cool! And that's a stunning shot at the end of the video with the sunset.
I think the polishing was particularly tricky for our manufacturer to work out how to do inexpensively - there being no flat faces makes some polishing techniques impossible.
I have been preoccupied with a very dumb question - or maybe not. Comments read with interest. Why don’t fair coins toss with repeatable patterns? Why are fair dice fair and ruled by statistics? I know the physics of what everyone says is the reason. But I am curious if there is a more fundamental reason and the implications on the universe . . . Crazy stupid question?
Oh, and by the way. It just occurred to me. If you happen to live near this lock smith, and need a lock smith when your wife has changed the locks to your home, because you've been a bad boy and deserve it, then I can recommend our sponsor and my best friend from the Casino...
It's basically an inflated d4 so it rolls a bit better. LEt's not pretend it's some ground breaking new shape you folks have just designed / discovered
You weren't lying about that one that rolls too much
lol I want that version dice
the suspense would kill me
Someone should start a game show with a set of those
Looks like the perfect Random Walk die to me
best ad i've ever seen on youtube at the end there
I like that you took the time to explain why a sphere would not make a good d4. 😂
Vernier calipers are great! They can be cheap, never run out of battery, and are accurate enough for 3d printing
Yeah, and still easy to buy and fairly cheap too, never really got the obsession with the digital ones that drift and can't measure accurately if they happen to go flat when the proper vernier ones just work
Vintage Brown & Sharpe - that caliper is a treasure! The engravings are immaculate
I like the crazy-rolling one.🐢
They also look far less painful to step on...
If I am not mistaken, you can take the Minkowski sum of two bodies of constant width and get another such body. So for smoothing you could just add a ball.
Your videos are always impressive, it’s a joy to see each thing you come up with next. Thanks Henry!
Awesome! I've designed and made (with resin moulding) some D4 dice that tumble more satisfyingly than standard D4 dice, but with all flat faces. That took a little bit of working out to get the way I wanted them, because there are a lot of options for how to go about it, but it is so satisfying to have them in hand. Needless to say, this video is delightful.
What shape did you use?
@@henryseg A few. Namely a tetrahedron base and also a prism base, but with cuts that create new faces which the die can't land on (on a level surface). I created more than one version of each, since there are different ways of doing it. I wouldn't know how to describe the ones that I ended up with specifically.
Great work Henry!
I feel like the lack of sharp corners provides the opportunity to do away with the slightly confusing multiple numbers per side aspect of traditional D4s. Surely the curve on the corner is smooth enough that you could just put one copy of each number right on the tip, right? I think that would be cool.
@@Canyon_Lark I think we were concerned that the numerals there, at the points with the most curvature, might be bad for rolling a book on top of them.
Orbiform d20 is just a sphere I reckon
An approximation of a sphere I reckon
If I've learned anything in physics, it's that at a certain level, everything is an approximation of a sphere
well I mean in a pure mathematical sense, of course there's a difference, but if you were to construct it, there would be no functional difference I mean
Utah mentioned on Pioneer Day!
Fantastic work
*ahem* d-fourbiform
Alternatively: Orbi-four-m. But that one doesn’t work so well in speech.
d4b4m.
you could print versions of these with white spots and the lack thereof in some corners, and they'd make for a neat re-skinned Royal Game of Ur ☆
how dare you combine two of my favorite things in one awesome idea. now i'm going to be thinking about this EMBARRASSINGLY often
Outstanding.
Imagine dice that also are rubik's cubes too.
i like that these are not only very cool dice, but also a great geometry deep-dive, due to manufacturing limitations regarding the reuleaux spheroform.
i got a truncated tetrahedron in my last dice lab order, so even though this would still roll much better, i can't justify a functionally similar purchase at the moment! very cool though!
Fascinating...Thank you for sharing
I have a need to buy these and I have no use for them….. love your videos.
Pretty weird to say that the sphere doesn't have the tetrahedral symmetry. It certainly does, and more. Of course its problem is that it won't stop rolling, which I would rather phrase perhaps as "doesn't have _only_ the tetrahedral symmetry".
At the Museum of Math in NYC you can ride in a rowboat over a small lake of these, and due to the constant width it's not a bumpy ride.
I think I was mentally thinking of it as “the symmetry group of the sphere is not the tetrahedral symmetry group”. But I see what you mean.
Shoutouts to Tim AND the locksmithy? Cool!
I love spinning dice! I'm the only person I know who can spin (normal tetrahedral) d4's.
That "rolls too well" shape actually tried to escape LMAO
What about other platonic orbiforms.
Great question! It isn’t clear if it will work with the other solids. You have to do some sort of average of shapes over the different symmetry transformations, and the worry is that it averages out to give you a sphere.
The tetrahedron has faces opposite vertices, while all the other Platonic solids have faces opposite faces, vertices opposite vertices. I reckon that rather spoils things.
@@jaapsch2 Maybe there are other symmetry groups with order divisible by the number of “sides” you want that would work?
@@henryseg I don't see how those can be made of constant width. The whole Reuleaux construction that leads to the Meissner tetrahedron relies on vertices being opposite the faces. If a polyhedron has opposite parallel faces, it seem to me the only way to make it of constant width is if both become spherical centred around the polyhedron centre, which defeats the purpose of a die. There might be something possible with odd bipyramids or even trapezohedra, but I'm not at all sure about that.
Very nice dice
I've been looking into the constant width shapes of four sides for the last couple of months. It seems odd to me because they were talked about on TH-cam about five years ago. Is there a more flexible way to model these with mathematical formulas other than with OpenSCAD?
Oh! Wonderful video.
Why didn't we have these when I had a D&D Wizard???
Could it be possible to find somewhere how to recreate the shape from Guifoyle and Klingenberg paper?
Your orbiform seems to have a center. Slice the orbiform with a plane through the center. You get a 2-dimensional shape of constant width. Could such a shape have n "sides" and "rotational symmetries" for n>3?
yeah check out a British 50p coin
0:10 I recommend the term "4 pointed dice"
0:43 - 0:51 that would've been true if there wasn't numbers impressed/stamped into the die
But they don't have points either, so "4 stable equilibria dice"
I've had a concept for a special d30 design that I've always wanted to see in action, and I even have a prototype modeled in Blender, but I lack the resources to actually manufacture or distribute it. Can I get in touch via business email, and discuss it under NDA?
Why would anyone use a d30? Genuinely curious
@@BallstinkBaron I used a d30 heavily as an aid to thinking while working on a particular projection from 6D to 3D. Outside of that there are sadly few games that use it... but it's a super pleasant shape (the rhombic d30 anyway -- imveryangry must have thought of a different way to do it).
@imveryangryitsnotbutter, I'm just guessing here but you may have trouble getting a mathematician under NDA. Not only is communicating insights their whole livelihood, but they're also part of a discipline that's already thought of lots of theoretical ways of making dice. You may want to have the NDA give them an "out" if your invention has already been written about.
@@dranorter Maybe an NDA is excessive. What I really mean is some kind of legal contract which says: "Do not sell this design on your store or share it with people who might try to sell it, unless you first pay me an amount of money up-front as compensation for my work (negotiable)." And I guess a clause stating "If you can prove that this design already existed before I proposed it, this contract is null and void."
d4 that isn't a lethal weapon
I need this
Man, Euler invented everything. Even when you think there's something new like "solids of constant width," nope, Euler ran down to the trademark office before you.
The yellow one looks delicious. Is it honey lemon or butterscotch?
Hard, brittle, plasticy, unfortunately!
the one that rolls too much is actually great... adds suspense
Does the weight of the paint effect the outcome? Visually, 3 and 4 look to have more surface area (more paint, more weight) than 1. Maybe this is a solved problem though and the manufacturing process uses a consistent amount of paint for each number?
If you want that level of precision in your dice, you’re looking at casino dice, which are milled rather than injection molded, and the pips filled in with material of the same density as the rest of the die. The impression I get is that there are far larger sources of error than amount of paint on different parts of an injection molded die!
@@henryseg thank you, cool project!
STL file please? The links in the description doesn't have it
Is it possible to get the 3D files for the printable version?
i found it interesting when you rolled a book on them. i have so many questions like for instance: can you rotate the book without losing grip of each dice to the floor and the book? how many degrees of freedom does rolling a book have on differently shaped dice? how many dice can you add under the book before rolling it becomes impossible? (without losing grip?)
it's just the same as rolling a book on spheres
@jon1758 are you sure? Im pretty sure the speed of the rolling isnt constant
0:53 that's your book!
the D forb
wait i don’t understand how this can be constant width?? someone please help me out here..
at a molecular level: I wonder if, if we were to roll it an infinity amount of time, if there wouldn't be a biased number due to the material not being 100% perfect all around, ain't no way all the molecules are arranged perfectly all the way. I'm sure on a small scale it's unnoticeable, but on a larger scale are dices a real way to obtain random numbers. Or could we expect a number to happen more frequently. It would made sense to me.
Right, no physical die will be perfectly fair.
Design a dice that has the most chaotic rolling
@wyrmwood has entered the chat.
i want a d6 :D
Wait... Are you.. what, ah. I didn't know you were so close! Aaaahhh! A local dice company! Now I have to share this with the local game shops I visit. So cool! And that's a stunning shot at the end of the video with the sunset.
I’m not usually based in Park City, I just happened to be passing through!
Ah, that makes sense. Still, it's rare to see Utah mentioned within TH-cam videos at all (unless I'm specifically looking for videos about the state)
I went straight to the website to buy some.. I couldn't do $9 each though, just fyi.
I think the polishing was particularly tricky for our manufacturer to work out how to do inexpensively - there being no flat faces makes some polishing techniques impossible.
I understand
A sphere with ball in tetrahedral void would have worked better.
The claim that a sphere doesn't possess tetrahedral symmetry doesn't ring true...
It has more than tetrahedral symmetry…
I have been preoccupied with a very dumb question - or maybe not.
Comments read with interest.
Why don’t fair coins toss with repeatable patterns? Why are fair dice fair and ruled by statistics? I know the physics of what everyone says is the reason. But I am curious if there is a more fundamental reason and the implications on the universe . . .
Crazy stupid question?
Oh no
Oh, and by the way. It just occurred to me. If you happen to live near this lock smith, and need a lock smith when your wife has changed the locks to your home, because you've been a bad boy and deserve it, then I can recommend our sponsor and my best friend from the Casino...
It's basically an inflated d4 so it rolls a bit better. LEt's not pretend it's some ground breaking new shape you folks have just designed / discovered