1) Construct a polyhedra with uneven weight distribution which is stable on exactly two faces.
2) Make one of those faces much more stable than the other, so if it is on the limited stability face and disturbed, it will switch to the high stability face.
A structure like that would be useful as a tamper detector.
For some reason he did not like my suggestion that he get a #1 billard ball.
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?
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.
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.
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.
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.