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In the past decade, significant effort has been devoted to the study of effective S = ½ triangular dimer and honeycomb lattice antiferromagnets containing the Co²⁺ cation. The restricted geometry of the triangular lattice, as well as proposed Kitaev-type interactions in honeycomb systems have both been shown to give rise to exotic spin dynamics, even below the bulk magnetic ordering transition. We present a new Co-based antiferromagnet, K₇Co₆Te₁₁O₄₆H_x, possessing a pseudo-hexagonal arrangement of cobalt cations in the ac-plane which dimerize along b, with chiral chains of K atoms filling the hexagonal channels. The material orders antiferromagnetically below T_N­ = 9 K, with ferrimagnetic correlations persisting up to T = 50 K. While the overall structure is more three-dimensional than other Co-based QSL candidates, it contains both the triangular dimer geometry of the Heisenberg-type systems and the overall pseudo-hexagonal pattern of the Ising-like phases. As such, it presents a unique opportunity to explore the interplay between the geometric and non-geometric frustration intrinsic to each model in a hybrid structure. Further development of this structure type to magnetically isolate two-dimensional layers would also offer a novel avenue for stabilizing spin liquid-like behavior.