Ca10(PO4)6CO3 is an `apatite' with pseudo-hexagonal symmetry with monoclinic space group Pb and lattice constants a = 9.557 (3) A, b ≃ 2a, c = 6.872 (2) A and γ = 120.36±0.04°.
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J. C. Elliott (1980) studied this question.