Single crystal X-ray examination has shown that högbomite forms a series of polytypes, designated nH or nR, with hexagonal or rhombohedral lattices and hexagonal unit-cell dimensions a 5·72 Å, c 4·6 × n Å. The polytypes arise by variation, in a manner as yet undetermined, of the stacking sequence of approximately close-packed oxygen layers with interstitial cations on fourfold and on sixfold sites; the composition of 1/nth of a unit-cell may be represented as R1·0−1·62+T0·2−0·44+R3·7−4·33+O7·6−8·02−(OH)0−0·4−, where R²⁺ = Zn, Fe, Mg, and R²⁺ = Fe, Al. The polytypes so far observed are 4H, 5H, 6H, 15H, 15R, and 18R. Minerals structurally related to högbomite are nigerite (3H) and taaffeite (4H). A new occurrence of högbomite, polytype 5H, with composition Ti_1·7Fe_1·6Mg_6·3Al_18·8Si_0·2O₄₀, is described from a spinel-free paragenesis in a magnesian skarn at Mautia Hill, Tanganyika. Another new occurrence in an aluminous xenolith in the Cashel gabbro in Co. Galway, Ireland, is recorded. X-ray powder data are given for two of the polytypes.