Integer triangle we today use the term Heronian triangle; Somos uses it to refer to triangles whose ratios of sides are rational; Conway and Guy define a rational triangle as one with rational sides and rational angles measured in degrees—in which case the only rational triangle is the rational-sided equilateral triangle. There are various general properties for an integer triangle, given in the first section below. All other sections refer to classes of integer triangles with specific properties. Any triple of positive integers can serve as the side lengths of an integer triangle as long as it satisfies the triangle inequality: the
Schwarz triangle function classification of arithmetic triangle groups (there are only finitely many) and determined when two of them are commensurable. The particular example is related to Bring's curve and the arithmetic theory implies that the triangle group for Δ contains the triangle group for the triangle Δ with angles /4, /4 and /5 as a non-normal subgroup of index 6. Doubling the triangles Δ and Δ, this implies that there should be a relation between 6 triangles Δ with angles /2, /5 and /5 and hyperbolic area /10 and a triangle Δ with angles /5, /5 and /10 and hyperbolic area 3/5.