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.
I first discovered the result computationally, using a program written in https://sentient-lang.org/, before finding the ‘human’ proof described in that PDF.
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!
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.
Or the edge so, the pipped face is 1, then go over that edge for 2, keep going around for 3 and 4. If we consider that "going east" then 5 is on the north pole.
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[ 3.3 ms ] story [ 50.4 ms ] threadHow 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.
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.
https://en.wikipedia.org/wiki/Razzle_(game)
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.
Only uses 6 pips.
Centre pip = 1, Edge = 2, Corner = 3
Put the pip on the face, but near the corner.
The comment above mine was using this terminology to refer to the corner of a face.