• These are Eisenstein triples. Similar to Pythagorean triples, but for 60-degree triangles, and they have their own Euclid formula as well.
  • This paper shows that if \((a, b, c)\) is a primitive triple, then \((b - a, b, c)\) is one too. Also any \(k>0\) multiple like \((ka, kb, kc)\) is an Eisenstein triple.
  • Finally, we can use the Euclid’s formula to generate the \((a, b, c)\) sets, then pull \({(b - a, b, c)}\) from them. Find the inradius \(r\), and \(k = 1053779 / r\).