Such a waste of faces :). Give a tetrahedron's faces 0,1,2, and 4 pips and throw it into a v-shaped groove so that it lands on an edge. (This is also a solution to numbering the corners of a cube).

So you get, with equal probabilities, 0+1, 0+2, 1+2, 0+4, 1+4, or 2+4 = {1,2,3,4,5,6}. Same as 2:07 in the video, but using only 1/3 of the faces. Brilliant!

I'm (pleasantly) surprised to see this on the front page of HN!

If anyone really wants to nerd out on the rhombic triacontahedral die, my proof of uniqueness is at https://s3.boskent.com/rhombic-triacontahedron-die/uniquenes...

I first discovered the result computationally, using a program written in https://sentient-lang.org/, before finding the ‘human’ proof described in that PDF.

This is glorious. What a world we live in.

How can we make a die that functions as a d6, but has "less pips". An elegant dodecahedron as the solution. Less pips but more sides. Not an economic solution, but I love that these problems are being solved.

That is the nerdiest thing I’ve ever seen and it’s appropriate that he was wearing a top hat while presenting it.

However, the point of dice is typically not so you can count the numbers but so others can count them. People sitting at a table with you cannot see “up”, they can only see from an angle and so these dice while mathematically cool are completely impractical. Great example of white tower design.

The article points this problem out. It's recreational mathematics, not intended to be practical.

Would be a feature not a bug for this "game"

https://en.wikipedia.org/wiki/Razzle_(game)

Or a d6 with the 4, 5 and 6 faces blank. When you roll, if the face isn't blank, that's your number. If it is then flip the die over and subtract that number from 7.

Only uses 6 pips.

Pip position encoding can get that down to 3. One pip on 3 adjacent sides.

Centre pip = 1, Edge = 2, Corner = 3

If we're gonna go that route, you can just put a single pip on a corner and derive all of the other positions from that.

Nope, that’s rotationally symmetric around the (pip, center of dice) axis.

Put the pip on the face, but near the corner.

This would be a fun video to send to your DM before showing up with these dice.

Oh no a boulder fell on your character. 200 points of crush damage.