We show how the Heronian triangle 13–14–15 sits at a common nodebetween four worlds: (i) the family of consecutive triangles(a−1,a,a+1) with integer area and inradius, governed by Pell equationsin the real quadratic field Q(√3); (ii) an exact periodic “corona crystal”in the Euclidean plane, whose wallpaper group is p6m and whose reflectionsubgroup is the Euclidean Coxeter triangle group Δ(2,3,6); (iii) the cyclotomicfield Q(ζ12), which contains both Q(√−3) and the biquadratic fieldQ(√2,√3) arising from Pell-type equations; and (iv) a CM elliptic curvewith j-invariant 0, on which the corona crystal defines a (2,3,6)-torsionconfiguration with coordinates in cyclotomic subfields of Q(ζ12). The real quadratic field Q(√3) appears as the intersection K1 ∩ K2 ofthe biquadratic field K1 = Q(√2,√3) and the cyclotomic fieldK2 = Q(ζ12), and plays the role of arithmetic node connecting Pellarithmetic, planar crystallography, CM elliptic curves, and cyclotomicGalois symmetry around the triangle 13–14–15.