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.
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.
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.