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.