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We study the ground-state properties of $$\prescript{6}{YY}{\text{He}}$$ double hyperon for $$\lla$$ and $$\ooa$$ nuclei in a three-body model $$(Y+Y+\alpha)$$. We solve two coupled Faddeev equations corresponding to three-body configurations $$(\alpha Y,Y)$$ and $$(YY, \alpha)$$ 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 $$\lla$$, using three $$\Lambda\Lambda$$ lattice interaction models, leads to a ground state binding energy in the domain $(-7.468, -7.804)$ MeV and the separations $$\langle r_{\Lambda-\Lambda} \rangle$$ and $$\langle r_{\alpha-\Lambda} \rangle$$ in the domains $(3.555, 3.629)$ fm and $(2.867 , 2.902 )$ fm, correspondingly. The binding energy of double-$$\Omega$$ hypernucleus $$\ooa$$ leads to $-67.21$ MeV and consequently to smaller separations $$\langle r_{\Omega-\Omega} \rangle = 1.521$$ fm and $$\langle r_{\alpha-\Omega} \rangle = 1.293 $$ fm. Besides the geometrical properties, we study the structure of ground-state wave functions and show that the main contributions are from the $s-$wave channels. Our results are consistent with the existing theoretical and experimental data.