User:2^67-1/New Hemipyth Nonsense

I challenge all of you XENners to find mathematical objects that bear some relation to hemipyth's ratios.

I'm going to start.

• The 24-cell with side length 1: it only has lengths of sqrt(1), sqrt(2), sqrt(3), and sqrt(4) between any two distinct vertices.
  • 96 sqrt(1) lengths, 72 sqrt(2) lengths, 96 sqrt(3) lengths, 12 sqrt(4) lengths