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We classify two classes of B_2-graded Lie algebras which have a secondcompatible grading by an abelian group A: (a) graded-simple Lie algebras for Atorsion-free and (b) division-A-graded Lie algebras. Our results describe thecentreless cores of a class of affine reflection Lie algebras, hence apply inparticular to the centreless cores of extended affine Lie algebras, theso-called Lie tori, for which we recover results of Allison-Gao and Faulkner.Our classification (b) extends a recent result of Benkart-Yoshii.  Both classifications are consequences of a new description of Jordan algebrascovered by a triangle, which correspond to these Lie algebras via theTits-Kantor-Koecher construction. The Jordan algebra classifications followfrom our results on graded-triangulated Jordan triple systems. They generalizework of McCrimmon and the first author as well as theOsborn-McCrimmon-Capacity-2-Theorem in the ungraded case.

Lie tori of type B_2 and graded-simple Jordan structures covered by a triangle