Measurement of singly Cabibbo-suppressed decays D⁰ → π⁰π⁰π⁰, π⁰π⁰η π⁰ηη and ηηη

Using a data sample of e⁺e⁻ collision data corresponding to an integrated luminosity of 2.93 fb⁻¹ collected with the BESIII detector at a center-of-mass energy of s=3.773GeV, we search for the singly Cabibbo-suppressed decays D⁰→π⁰π⁰π⁰, π⁰π⁰η π⁰ηη and ηηη using the double tag method. The absolute branching fractions are measured to be B(D⁰→π⁰π⁰π⁰)=(2.0±0.4±0.3)×10⁻⁴, B(D⁰→π⁰π⁰η)=(3.8±1.1±0.7)×10⁻⁴ and B(D⁰→π⁰ηη)=(7.3±1.6±1.5)×10⁻⁴ with the statistical significances of 4.8σ 3.8σ and 5.5σ respectively, where the first uncertainties are statistical and the second ones systematic. No significant signal of D⁰→ηηη is found, and the upper limit on its decay branching fraction is set to be B(D⁰→ηηη)<1.3×10⁻⁴ at the 90% confidence level.