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Single crystals of Ba8CoRh6O21 were grown out of a potassium carbonate flux. The structure was solved by a general method using the superspace group approach. The superspace group employed was R3m(00γ)0s with a = 10.0431(1) Å, c1 = 2.5946(1) Å and c2 = 4.5405(1) Å, V = 226.60(1) Å3. Ba8CoRh6O21 represents the first example of an m = 5, n = 3 member of the A3n+3mA'nB3m+nO9m+6n family of 2H hexagonal perovskite related oxides and contains chains consisting of six consecutive RhO6 octahedra followed by one distorted CoO6 trigonal prism. These chains in turn are separated from each other by [Ba] chains.

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