\begin{document}$ {}_{YY }^{\;\;\;6}{\rm{He}} $\end{document} double hyperon for \begin{document}$ {}_{\Lambda\Lambda }^{\;\;\;6}{\rm{He}} $\end{document} and \begin{document}$ {}_{\Omega\Omega }^{\;\;\;6}{\rm{He}} $\end{document}nuclei in a three-body model \begin{document}$ (Y+Y+\alpha) $\end{document}. We solve two coupled Faddeev equations corresponding to the three-body configurations \begin{document}$ (\alpha Y, Y) $\end{document} and \begin{document}$ (YY, \alpha) $\end{document} in configuration space with the hyperspherical harmonics expansion method by employing the most recent hyperon-hyperon interactions obtained from lattice QCD simulations. Our numerical analysis for \begin{document}$ {}_{\Lambda\Lambda }^{\;\;\;6}{\rm{He}} $\end{document}, using three \begin{document}$ \Lambda\Lambda $\end{document} lattice interaction models, leads to a ground state binding energy in the \begin{document}$ (-7.468, -7.804) $\end{document}MeV domain and the separations \begin{document}$ \langle r_{\Lambda-\Lambda} \rangle $\end{document}and \begin{document}$ \langle r_{\alpha-\Lambda} \rangle $\end{document} in the domains of\begin{document}$ (3.555, 3.629) $\end{document} fm and \begin{document}$ (2.867 , 2.902 ) $\end{document} fm, respectively. The binding energy of the double-\begin{document}$ \Omega $\end{document} hypernucleus \begin{document}$ {}_{\Omega\Omega }^{\;\;\;6}{\rm{He}} $\end{document} leads to \begin{document}$ -67.21 $\end{document} MeV and consequently to smaller separations \begin{document}$ \langle r_{\Omega-\Omega} \rangle = 1.521 $\end{document} fm and \begin{document}$ \langle r_{\alpha-\Omega} \rangle = 1.293 $\end{document} fm. In addition to geometrical properties, we study the structure of ground-state wave functions and show that the main contributions are from the \begin{document}$ s- $\end{document}wave channels. Our results are consistent with the existing theoretical and experimental data."> Three-body Faddeev calculations for <inline-formula><tex-math id="M1">\begin{document}${{}_{\boldsymbol\Lambda \boldsymbol\Lambda }^{\;\;\;\;\bf 6}{\bf{He}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/862e8370-3bc5-40ac-87ab-bc194e778b78/CPC-2022-0164_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/862e8370-3bc5-40ac-87ab-bc194e778b78/CPC-2022-0164_M1.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}${{}_{\boldsymbol\Omega \boldsymbol\Omega }^{\;\;\;\;\bf 6}{\bf{He}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/862e8370-3bc5-40ac-87ab-bc194e778b78/CPC-2022-0164_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/862e8370-3bc5-40ac-87ab-bc194e778b78/CPC-2022-0164_M2.png"/></alternatives></inline-formula> hypernuclei -
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