Almost regular integer hexagons (Q753141)

An equiangular integer hexagon is a hexagon whose interior angles are all 120\(\circ\) and whose six sides and nine diagonals all have integer lengths. The author proves the following results: (i) there exists an infinite sequence of integers \(a_ n\) such that there is a sequence of equiangular integer hexagons with alternating sides of length \(a_ n\) and \(a_ n+1;\) (ii) there exists an infinite sequence of integers \(b_ n\) such that there is a sequence of equiangular integer hexagons with alternating sides of length \(b_ n\) and \(b_ n+2.\)