<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>Σ</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:mrow></mml:math>at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>514</mml:mn><mml:mo>–</mml:mo><mml:mn>750</mml:mn><mml:mspace width="0.3em"/><mml:mi mathvariant="normal">MeV</mml:mi><mml:mo>∕</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:math>and comparison with other<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:mrow></mml:math>production

Reaction ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\Sigma}}^{0}$ was measured with the Crystal Ball multiphoton spectrometer at eight ${K}^{\ensuremath{-}}$ momenta from 514 to $750\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕c$. Dynamics and the energy dependence of the reaction are shown by Dalitz plots, invariant mass spectra, production angular distributions, and total cross sections. The dipion invariant-mass spectra for ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\Sigma}}^{0}$ show an enhancement in the low mass region; the opposite is the case for the ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}\ensuremath{\Lambda}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}n$ reactions. There is no direct evidence for a ${f}_{0}(600)$-meson contribution to ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ production. Everywhere ${\ensuremath{\sigma}}_{t}({K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\Sigma}}^{0})⪡{\ensuremath{\sigma}}_{t}({K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}\ensuremath{\Lambda})$.