Dalitz plot analysis of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

A Dalitz plot analysis of approximately 12 500 ${D}^{0}$ events reconstructed in the hadronic decay ${D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{+}{K}^{\ensuremath{-}}$ is presented. This analysis is based on a data sample of $91.5\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected with the BABAR detector at the PEP-II asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ storage rings at SLAC running at center-of-mass energies on and 40 MeV below the $\ensuremath{\Upsilon}(4S)$ resonance. The events are selected from ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}c\overline{c}$ annihilations using the decay ${D}^{*+}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\pi}}^{+}$. The following ratio of branching fractions has been obtained: $BR=\frac{\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{+}{K}^{\ensuremath{-}})}{\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})}=(15.8\ifmmode\pm\else\textpm\fi{}0.1(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.5(\mathrm{syst}.))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}.$ Estimates of fractions and phases for resonant and nonresonant contributions to the Dalitz plot are also presented. The ${a}_{0}(980)\ensuremath{\rightarrow}\overline{K}K$ projection has been extracted with little background. A search for $CP$ asymmetries on the Dalitz plot has been performed.

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