Using 1310.6 × 10 6 J=ψ and 447.9 × 10 6 ψð3686Þ events collected with the BESIII detector at the BEPCII e þ e − collider, the branching fractions and the angular distributions of J=ψ and ψð3686Þ decays to ΛΛ and Σ 0Σ0 final states are measured. The branching fractions are determined, with much improved precision, to be 19.43 AE 0.03 AE 0.33, 11.64 AE 0.04 AE 0.23, 3.97 AE 0.02 AE 0.12 and 2.44 AE 0.03 AE 0.11 for J=ψ → ΛΛ, J=ψ → Σ 0Σ0 , ψð3686Þ → ΛΛ and ψð3686Þ → Σ 0Σ0 , respectively. The polar angular distributions of ψð3686Þ decays are measured for the first time, while those of J=ψ decays are measured with much improved precision. In addition, the ratios of branching fractions
Bðψð3686Þ→ΛΛÞBðJ=ψ→ΛΛÞ and Bðψð3686Þ→Σ 0Σ0 Þ BðJ=ψ→Σ 0Σ0 Þ are determined to test the "12% rule."