Est. 1998 — 27 years of woodworking knowledge
Tuesday Puzzle
A bit of solid geometry today.
A fair die is defined as one in which every numbered side has an equal probability of coming up. If we set the criteria for a fair die as all faces are identical in shape and size, all sides are equal in length, and all angles are equal, what shapes fit this criteria? hint: There are only 5 shapes that fit and the commonly seen cube is obviously one of them.
As a bonus, identify a shape that would make a fair die that does not meet the criteria.
Re: Tuesday Puzzle
I immediately identified two, then happened on the complete answer when checking my suspicion that one may relate to an unusual confluence of the worlds of architecture and chemistry.
I have a solution for the bonus question (there are infinitely many), but will hold off.
Re: Tuesday Puzzle
I always have trouble remembering #3.
Bucky Fuller was fond of #1. The #2 is well known. I once had a desk calendar in the shape of #4 and #5 has the same shape sides as #1 and #3.
Re: Tuesday Puzzle
The five solids named (as a group) after Socrates' most famous student are the ones that fit the criteria.
But when it comes to shapes that can be fair dice, there are more, many more.
answer
Holding strictly to the criteria, there are 5 shapes that qualify:
4 sides : the tetrahedron
6 sides: the cube (or hexahedron)
8 sides: the octahedron
12 sides: the dodecahedron
20 sides: the icosahedron
Re: answer *LINK*
Here is a link to a web page of the Mathematical Association of America.
It contains nice pictures of the five.
It also contains pictures of the isohedral solids, which are fair,
but do not satisfy the criteria (in other words, they are not platonic solids).
Fair Dice
Great article