Magic 8 Ball ( en.m.wikipedia.org )

Bassman1805 , 28 days ago (edited 27 days ago)

Each response is on an equilateral triangle face, so the die inside must be either a tetrahedron, octahedron, or a icosahedron (d4, d8 or d20). There are no other regular polyhedrons composed of equilateral triangles.

Doesn't take too many attempts to see more than 4 answers, so it can't be the tetrahedron. It might take a large number of attempts to get the 9th unique response, but if you look carefully you can sort of see the adjacent faces while the die settles. Not well enough to read, but well enough to get an idea of the angle between the faces. Too shallow to be an octahedron, so it must be a dodecahedron.

OlinOfTheHillPeople , 28 days ago

https://qph.cf2.quoracdn.net/main-qimg-3420ec5df7b5441b01d6748a62c74176-lq

altima_neo , 27 days ago

And apparently cast in two halves that are snap fit together

Scubus , 27 days ago

I feel like I saw a d100 composed of equilateral triangles. Is there an algorithm that determines whether a shape can be composed of equalateral triangles? I'd ask for a proof but I fucking hate proofs.

Bassman1805 , 27 days ago

There are only 5 polyhedrons that can be made from regular polygons. They're called the Platonic Solids.

Tetrahedron (triangle), cube (square), octahedron (triangle), dodecahedron (pentagon), icosahedron (triangle)

davidagain , 6 days ago

Not a proof, but a thought experiment. Imagine you have a bunch of equilateral triangles made of plastic that have mangetout sides so they stick to each other. How many can you have around a point?

Two triangles just stick to each other flat and you don't get a 3D shape.

Three triangles makes the top of a triangular pyramid and you can add one more on the base to get a tetrahedron.

Four triangles makes the top of a square based pyramid and you can make another one like that and put it underneath, giving you an octahedron.

Five triangles makes the top of a pentagonal based pyramid. You could make another one and stick it underneath, but it wouldn't be regular because the top and bottom points would be surrounded by five triangles whereas the ones on the sides would be surrounded by just four. The trick here is to make a band of ten additional triangles pointing up, down, up down etc to go between the two layers. Then two triangles from the top layer touch at a point where a down, up, down junction is and you get five triangles around the point there too. Same for the bottom layer. Now you have an icosahedron.

Six triangles makes a flat plane and you'll just tile a surface rather than make a solid.

Seven or more triangles is too many to even lie flat and it'll go all wrinkly on the large scale.

You may be thinking of a D60 dice, which is based on a stellated dodecahedron - stick three pentagons together at each point but turn each pentagon into the base of a small pentagonal based pyramid. It's not regular because the points don't all have the same number of sides touching them, but it is very pretty and rolls very nicely.

henfredemars , 28 days ago

Really? Appreciate your sharing some interesting details.