User:2^67-1/New Hemipyth Nonsense

NO I AM NOT STARTING A CULT

Not coincidences

• 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 (all 3-smooth numbers!)
  • Total edge lengths are 96, total area is 24*sqrt(3), total cell volume is 8*sqrt(2), total volume is 2.
• Matt Parker calling 2 and 3 subprimes and 2 and 3 literally forming the bedrock of almost every 'natural' JI system (I agree with him)
• The truncated Spiral of Theodorus

Coincidences

• EulerGamma ≈ 1/sqrt(3)
• QPochhammer[1/2] ≈ 1/sqrt(12)