You jest, but I knew a DND player with a dice addicting that loved showing off his D-1 Mobius strip dice - https://www.awesomedice.com/products/awd101?variant=45578687...
For some reason he did not like my suggestion that he get a #1 billard ball.
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There's a link to a D2, where prior to clicking I was thinking "well that's a coin, right?" until I realised a coin is technically a (very biased) D3.
Huh, now I'm curious, what did the D2 look like?
Lenticoidal, I guess? I.e. remove the outer face of the cilinder by making the faces curved
Yeah, that was my thought as well, but that's also basically a D3 with a really small third edge, in practice. I was wondering whether there's some clever shape that actually is a D2, though maybe that's a Möbius strip in reality.
> with a really small third edge
Doesn't every die have a bunch of edges or even vertices that aren't considered faces despite having a measurable width? As long as it's realistically impossible to land on that edge, I think it shouldn't count as a face.
> what did the D2 look like
> though maybe that's a Möbius strip in reality.
You're close, it looks like a failed attempt at doing a möbius ring.
Love it - any sphere will do.
A ping pong ball would be great - the DM/GM could throw it at a player for effect without braining them!
(billiard)
> the DM/GM could throw it at a player for effect without braining them!
If you're prepared to run over to wherever it ended up after that, sure.
I learned to juggle with ping pong balls. Their extreme lightness isn't an advantage. One of the most common problems you have when learning to juggle is that two balls will collide. When that happens with ping pong balls, they'll fly right across the room.
A sphere is bad, it rolls away. The shape from the article would be better, but it is too hard to manufacture. And weighting is cheating anyway. The best option for a D1 is probably the gömböc, which is mentioned in the article.
Technically, a gomboc is a D1.00…001.
Any normal die could also land on an edge.
It’s infinitely unlikely to do so, a set of measure zero.
Just as with the gömböc. Though the latter balances on only one unstable axis while a D6 die does so on 20 (12 edges and 8 vertices).
Vertices aren't axes! They have the wrong dimensionality.
Nitpick: one of the properties of dice is that they stop on one side (i.e they converge towards stable rest on even ground) and the typical rule is that when they come at rest because of something other than even ground then the throw is invalid.
So while a sphere has only one side it basically never comes at a stable enough rest unless stopped by uneven ground (invalid throw), and if it stops because of friction it is unstable rest where the slightest nudge would make it roll again.
Therefore in a sense a sphere only works as a 1D because you know the outcome before throwing.
Edge cases are fun.
Yes, it’s more like a D0.
It’s debatable though whether a sphere can constitute an edge case. ;)
> Love it - any sphere will do.
That's basically what the link shows. A Möbius strip is interesting in that it is a two-dimensional surface with one side. But the product is three-dimensional, and has rounded edges. By that standard, any other die is also a d1. The surface of an ordinary d6 has two sides - but all six faces that you read from are on the same one of them.
Or any mobius strip
I think a spherical D1 is far more interesting than a Möbius strip in this case.
Dn: after the Platonic solids, Dn generally has triangular facets and as n increases, the shape of the die tends towards a sphere made up of smaller and smaller triangular faces. A D20 is an icosahedron. I'm sure I remember a D30 and a D100.
However, in the limit, as the faces tend to zero in area, you end up with a D1. Now do you get a D infinity just before a D1, when the limit is nearly but not quite reached or just a multi faceted thing with a lot of countable faces?
> However, in the limit, as the faces tend to zero in area, you end up with a D1.
Not really. You end up with a D-infinity, i.e. a sphere. A theoretical sphere thrown randomly onto a plane is going to end up with one single point, or face, touching the plane, and the point or face directly opposite that pointing up. Since in the real world we are incapable of distinguishing between infinitesimally small points, we might just declare them all to be part of the same single face, but from a mathematical perspective a collection of infinitely many points that are all equidistant from a central point in 3-dimensional space is a sphere.
That's like saying a donut only has one side.
The linked die seems similar to this: https://cults3d.com/en/3d-model/game/d1-one-sided-die which seems adjacent to a Möbius strip but kinda isn't because the loop is not made of a two sided flat strip. https://wikipedia.org/wiki/M%C3%B6bius_strip
Might be an Umbilic torus: https://wikipedia.org/wiki/Umbilic_torus
The word side is unclear.
Everyone knows that a donut has two sides.
Inside, and outside.
I've always seen a D1 as a bingo ball...
You sunk my battleship!